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Recent questions and answers in Combinatory
368
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Kenneth Rosen Edition 7 Exercise 6.1 Question 50 (Page No. 398)
How many bit strings of length $10$ contain either five consecutive $0s$ or five consecutive $1s?$
How many bit strings of length $10$ contain either five consecutive $0s$ or five consecutive $1s?$
Sahil5635
Sahil5635
answered
May 13
Combinatory
kenneth-rosen
discrete-mathematics
counting
descriptive
+
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107
views
0
answers
1
votes
Counting
Suppose that there are nine students in a discrete mathematics class at a small college. a) Show that the class must have at least five male students or at least five female students. b) Show that the class must have at least three male students or at least seven female students.
Suppose that there are nine students in a discrete mathematics class at a smallcollege.a) Show that the class must have at least five male students or at least five femal...
Nini
Nini
asked
May 6
Combinatory
discrete-mathematics
combinatory
+
–
18.4k
views
11
answers
44
votes
GATE CSE 2016 Set 2 | Question: 29
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
yudhistar
yudhistar
answered
Apr 25
Combinatory
gatecse-2016-set2
modular-arithmetic
normal
numerical-answers
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658
views
1
answers
0
votes
Kenneth Rosen Edition 7 Exercise 6.1 Question 32 (Page No. 397)
How many strings of eight uppercase English letters are there if letters can be repeated? if no letter can be repeated? that start with $X,$ if letters can be repeated? that start with $X,$ if no letter can be repeated? that ... can be repeated? that start or end with the letters $BO$ (in that order), if letters can be repeated?
How many strings of eight uppercase English letters are thereif letters can be repeated?if no letter can be repeated?that start with $X,$ if letters can be repeated?that ...
aswinik
aswinik
answered
Apr 8
Combinatory
kenneth-rosen
discrete-mathematics
counting
descriptive
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1.3k
views
2
answers
0
votes
Kenneth Rosen Edition 7 Exercise 6.1 Question 57 (Page No. 398)
The name of a variable in the JAVA programming language is a string of between $1$ and $65,535$ characters, inclusive, where each character can be an uppercase or a lowercase letter, a dollar sign, an underscore, or a digit, except that the first character must not be a digit. Determine the number of different variable names in JAVA.
The name of a variable in the JAVA programming language is a string of between $1$ and $65,535$ characters, inclusive, where each character can be an uppercase or a lower...
Shriram BM
Shriram BM
answered
Mar 3
Combinatory
kenneth-rosen
discrete-mathematics
counting
descriptive
+
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8.2k
views
4
answers
7
votes
GATE CSE 2023 | Question: 5
The Lucas sequence $L_{n}$ is defined by the recurrence relation: \[ L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3, \] with $L_{1}=1$ and $L_{2}=3$ ... $L_{n}=\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}$
The Lucas sequence $L_{n}$ is defined by the recurrence relation:\[L_{n}=L_{n-1}+L_{n-2}, \quad \text { for } \quad n \geq 3,\]with $L_{1}=1$ and $L_{2}=3$.Which one of t...
Priyam Garg
Priyam Garg
answered
Feb 27
Combinatory
gatecse-2023
combinatory
recurrence-relation
1-mark
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18.6k
views
18
answers
19
votes
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
The value of $3^{51} \text{ mod } 5$ is _____
ravi2002
ravi2002
answered
Feb 26
Combinatory
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
1-mark
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–
1.6k
views
4
answers
2
votes
ACE Test Series: Generating Function
The generating function of the sequence $\left \{ a_{0},a_{1},a_{2}..........a_{n}………...\infty \right \}$ where $a_{n}=\left ( n+2 \right )\left ( n+1 \right ).3^{n}$ is $a)3\left ( 1+3x \right )^{-2}$ $b)3\left ( 1-3x \right )^{-2}$ $c)2\left ( 1+3x \right )^{-3}$ $d)2\left ( 1-3x \right )^{-3}$
The generating function of the sequence $\left \{ a_{0},a_{1},a_{2}..........a_{n}………...\infty \right \}$where $a_{n}=\left ( n+2 \right )\left ( n+1 \right ).3^{n}...
Priyam Garg
Priyam Garg
answered
Feb 20
Combinatory
generating-functions
discrete-mathematics
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–
4.8k
views
6
answers
24
votes
TIFR CSE 2012 | Part A | Question: 7
It is required to divide the $2n$ members of a club into $n$ disjoint teams of $2$ members each. The teams are not labelled. The number of ways in which this can be done is: $\frac{\left ( 2n \right )!}{2^{n}}$ $\frac{\left ( 2n \right )!}{n!}$ $\frac{\left ( 2n \right )!}{2^n . n!}$ $\frac{n!}{2}$ None of the above
It is required to divide the $2n$ members of a club into $n$ disjoint teams of $2$ members each. The teams are not labelled. The number of ways in which this can be done ...
Priyam Garg
Priyam Garg
answered
Feb 18
Combinatory
tifr2012
combinatory
balls-in-bins
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5.0k
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2
answers
0
votes
Kenneth Rosen Edition 7 Exercise 6.3 Question 26 (Page No. 414)
Thirteen people on a softball team show up for a game. How many ways are there to choose $10$ players to take the field? How many ways are there to assign the $10$ positions by selecting players from the $13$ people who show ... ways are there to choose $10$ players to take the field if at least one of these players must be a woman?
Thirteen people on a softball team show up for a game.How many ways are there to choose $10$ players to take the field?How many ways are there to assign the $10$ position...
Priyam Garg
Priyam Garg
answered
Feb 11
Combinatory
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
+
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239
views
0
answers
0
votes
Combinatorics & Probability
A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone, and so on. A person can pass the rumor on to anyone except the individual who just called. (a) By how many different paths can a rumor ... in $N$ calls? (c) What is the probability that if $A$ starts the rumor, then $A$ receives the third calls?
A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone, and so on. A person can pass the rumor on to anyo...
Debargha Mitra Roy
Debargha Mitra Roy
asked
Feb 8
Combinatory
combinatory
counting
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644
views
2
answers
6
votes
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 56
The coefficient of $x^6$ in the expansion of $A(x)$ is, where $ A(x)=\frac{x(1+x)}{(1-x)^3} $
The coefficient of $x^6$ in the expansion of $A(x)$ is, where$$A(x)=\frac{x(1+x)}{(1-x)^3}$$
squirrel69
squirrel69
answered
Feb 6
Combinatory
goclasses2024-mockgate-14
numerical-answers
combinatory
recurrence-relation
2-marks
+
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260
views
1
answers
0
votes
#self doubt
Can someone please explain the following case of combination I means identical D means different DOIB with boxes being empty and non empty As in this question the given value in question itself i am not able to interpret. https://gateoverflow.in/420251/go-classes-test-series-2024-mock-gate-test-12-question-17
Can someone please explain the following case of combinationI means identicalD means different DOIB with boxes being empty and non emptyAs in this question the given valu...
GauravRajpurohit
GauravRajpurohit
answered
Jan 31
Combinatory
discrete-mathematics
+
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716
views
1
answers
4
votes
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 30
A university's mathematics department has $10$ professors and will offer $20$ different courses next semester. Each professor will be assigned to teach exactly $2$ of the courses, and each course will have exactly one professor assigned to teach it. If any ... $10^{20}-2^{10}$ $\dfrac{20 ! 10 !}{2^{10}}$
A university's mathematics department has $10$ professors and will offer $20$ different courses next semester. Each professor will be assigned to teach exactly $2$ of the...
SankarVinayak
SankarVinayak
answered
Jan 29
Combinatory
goclasses2024-mockgate-13
goclasses
combinatory
counting
1-mark
+
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972
views
4
answers
0
votes
Computer Science - UGC NET 2021 [ Question ID = 2353 ]
How many ways are there to assign 5 different jobs to 4 different employees if every employee is assigned at least 1 job ? 1024 625 240 20
How many ways are there to assign 5 different jobs to 4 different employees if every employee is assigned at least 1 job ?1024 625 240 20
swapnil8222
swapnil8222
answered
Jan 25
Combinatory
discrete-mathematics
permutation-and-combination
engineering-mathematics
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977
views
2
answers
6
votes
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 17
The number of ways that one can divide $10$ distinguishable objects into $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the piles are also distinguishable?
The number of ways that one can divide $10$ distinguishable objects into $3$ indistinguishable non-empty piles, is:$$\left\{\begin{array}{c}10 \\3\end{array}\right\}=9330...
krishnajsw
krishnajsw
answered
Jan 21
Combinatory
goclasses2024-mockgate-12
goclasses
numerical-answers
combinatory
counting
1-mark
+
–
1.0k
views
2
answers
5
votes
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 18
The number of ways that one can divide $10$ distinguishable objects in $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the objects are also indistinguishable?
The number of ways that one can divide $10$ distinguishable objects in $3$ indistinguishable non-empty piles, is:$$\left\{\begin{array}{c}10 \\3\end{array}\right\}=9330$$...
GauravRajpurohit
GauravRajpurohit
answered
Jan 21
Combinatory
goclasses2024-mockgate-12
goclasses
numerical-answers
combinatory
counting
1-mark
+
–
221
views
1
answers
1
votes
selfdoubt combinatory
In how many ways can you distribute 4 different choclates to 3 people such that each gets atleast 1 choclate.
In how many ways can you distribute 4 different choclates to 3 people such that each gets atleast 1 choclate.
swapnil8222
swapnil8222
answered
Jan 14
Combinatory
self-doubt
made-easy-test-series
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610
views
2
answers
7
votes
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 44
Acceptable input for a certain pocket calculator is a finite sequence of characters each of which is either a digit or a sign. The first character must be a digit, the last character must be a digit, and any character that is a sign must be followed by a digit. There ... by $N_k=a N _{k-1}+b N _{k-2}$, for $k \geq 3$. What is $a+ b?$
Acceptable input for a certain pocket calculator is a finite sequence of characters each of which is either a digit or a sign. The first character must be a digit, the la...
Sujith48
Sujith48
answered
Jan 14
Combinatory
goclasses2024-mockgate-11
goclasses
numerical-answers
combinatory
recurrence-relation
2-marks
+
–
12.6k
views
7
answers
38
votes
GATE CSE 1999 | Question: 2.2
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves? $1638$ $2100$ $2640$ None of the above
Two girls have picked $10$ roses, $15$ sunflowers and $15$ daffodils. What is the number of ways they can divide the flowers among themselves?$1638$$2100$$2640$None of th...
yuyutsu
yuyutsu
answered
Jan 9
Combinatory
gate1999
combinatory
normal
+
–
7.5k
views
8
answers
34
votes
GATE CSE 2002 | Question: 13
In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of $2$ positive integers (which are not necessarily distinct). For example, for $n=3$, the number of ways is $2$, i.e., $1+2, 2+1$. Give only ... $n \geq k$ be expressed as the sum of $k$ positive integers (which are not necessarily distinct). Give only the answer without explanation.
In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of $2$ positive integers (which are not necessarily distinct). For example, for $n=3$, th...
GauravRajpurohit
GauravRajpurohit
answered
Dec 26, 2023
Combinatory
gatecse-2002
combinatory
normal
descriptive
balls-in-bins
+
–
455
views
1
answers
0
votes
Kenneth Rosen Edition 7 Exercise 8.2 Question 48 (Page No. 526)
Some linear recurrence relations that do not have constant coefficients can be systematically solved. This is the case for recurrence relations of the form $f (n)a_{n} = g(n)a_{n-1} + h(n).$ Exercises $48-50$ ...
Some linear recurrence relations that do not have constant coefficients can be systematically solved. This is the case for recurrence relations of the form $f (n)a_{n} = ...
cc_flow
cc_flow
answered
Dec 25, 2023
Combinatory
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
+
–
8.4k
views
6
answers
33
votes
GATE CSE 2000 | Question: 5
A multiset is an unordered collection of elements where elements may repeat any number of times. The size of a multiset is the number of elements in it, counting repetitions. What is the number of multisets of size $4$ that can be ... n distinct elements so that at least one element occurs exactly twice? How many multisets can be constructed from n distinct elements?
A multiset is an unordered collection of elements where elements may repeat any number of times. The size of a multiset is the number of elements in it, counting repetiti...
This_is_Nimishka
This_is_Nimishka
answered
Dec 14, 2023
Combinatory
gatecse-2000
combinatory
normal
descriptive
+
–
280
views
1
answers
0
votes
Self Doubt on Combinatory Discrete Mathematics
Given there are 3 full baskets of apples, mangoes, and oranges. How many ways possible if a) You need to buy any 4 fruits out of these 3 baskets ? b) you buy any 4 fruits such that you take at least one from each basket ?
Given there are 3 full baskets of apples, mangoes, and oranges. How many ways possible ifa) You need to buy any 4 fruits out of these 3 baskets ?b) you buy any 4 fruits s...
Negan
Negan
answered
Dec 3, 2023
Combinatory
discrete-mathematics
combinatory
+
–
225
views
1
answers
0
votes
#self doubt
The number of bit strings of length 8 that will either start with 1 or end with 00 is? (https://gateoverflow.in/15898/isro2014-19) In the ‘either or’ case we will include the ‘and’ case also? means: 1 string starting with 1 2 stating ending with 00 3 strings start with 1 and end with 00 all above cases will be included in either or case or only 1,2 will be included?
The number of bit strings of length 8 that will either start with 1 or end with 00 is? (https://gateoverflow.in/15898/isro2014-19)In the ‘either or’ case we will incl...
yahba
yahba
answered
Nov 20, 2023
Combinatory
combinatory
+
–
308
views
0
answers
0
votes
how many it string of length 10 over the alphabet {a,b,c} have either exactly three a's or exactly four b's
_shreya123
_shreya123
asked
Nov 18, 2023
Combinatory
combinatory
strings
+
–
6.9k
views
3
answers
14
votes
GATE CSE 2023 | Question: 38
Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|=|B|=k$ and $A \cap B=\emptyset$. We say that a permutation of $U$ separates $A$ from $B$ if ... $2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k !)^{2}$
Let $U=\{1,2, \ldots, n\},$ where $n$ is a large positive integer greater than $1000.$ Let $k$ be a positive integer less than $n$. Let $A, B$ be subsets of $U$ with $|A|...
ssingla
ssingla
answered
Nov 9, 2023
Combinatory
gatecse-2023
combinatory
counting
2-marks
+
–
337
views
1
answers
0
votes
Kenneth Rosen Edition 7 Exercise 6.5 Question 40 (Page No. 433)
How many ways are there to travel in $xyzw$ space from the origin $(0, 0, 0, 0)$ to the point $(4, 3, 5, 4)$ by taking steps one unit in the positive $x,$ positive $y,$ positive $z,$ or positive $w$ direction?
How many ways are there to travel in $xyzw$ space from the origin $(0, 0, 0, 0)$ to the point $(4, 3, 5, 4)$ by taking steps one unit in the positive $x,$ positive $y,$ p...
Vandana04
Vandana04
answered
Oct 22, 2023
Combinatory
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
+
–
546
views
4
answers
2
votes
Permutation and Combination
In how many ways can 3 non-negative integers be chosen such that a + b + c = 10 where a >= -1 , b >= -5 and c >= 3 ? 36 66 105 None
In how many ways can 3 non-negative integers be chosen such that a + b + c = 10 where a >= -1 , b >= -5 and c >= 3 ? 3666105None
Zuleen Khan
Zuleen Khan
answered
Oct 21, 2023
Combinatory
combinatory
discrete-mathematics
+
–
446
views
1
answers
0
votes
Combinatorics, Discrete Maths (self doubts)
Consider the set of 4 -digit positive integers. How many of them have their digits in :- a) strictly decreasing order ? b) non decreasing order ? c) non increasing order ?
Consider the set of 4 -digit positive integers. How many of them have their digits in :-a) strictly decreasing order ?b) non decreasing order ?c) non increasing order ?...
Abhay123
Abhay123
answered
Oct 20, 2023
Combinatory
combinatory
sorting
discrete-mathematics
goclasses
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–
12.4k
views
6
answers
27
votes
GATE CSE 2021 Set 2 | Question: 50
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
akshay_123
akshay_123
answered
Oct 4, 2023
Combinatory
gatecse-2021-set2
combinatory
counting
numerical-answers
2-marks
+
–
339
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1
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0
votes
Kenneth Rosen Edition 7 Exercise 6.3 Question 39 (Page No. 415)
How many license plates consisting of three letters followed by three digits contain no letter or digit twice?
How many license plates consisting of three letters followed by three digits contain no letter or digit twice?
Vijay111
Vijay111
answered
Oct 1, 2023
Combinatory
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
+
–
783
views
1
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0
votes
Kenneth Rosen Edition 7 Exercise 6.3 Question 38 (Page No. 414)
How many ways are there to select $12$ countries in the United Nations to serve on a council if $3$ are selected from a block of $45, 4$ are selected from a block of $57,$ and the others are selected from the remaining $69$ countries?
How many ways are there to select $12$ countries in the United Nations to serve on a council if $3$ are selected from a block of $45, 4$ are selected from a block of $57,...
Vijay111
Vijay111
answered
Oct 1, 2023
Combinatory
kenneth-rosen
discrete-mathematics
counting
combinatory
descriptive
+
–
499
views
2
answers
2
votes
GoClasses Youtube
Determine the Number of $6$ digit integers (no leading zeroes) in which no digit is repeated and its divisible by $4$.
Determine the Number of $6$ digit integers (no leading zeroes) in which no digit is repeated and its divisible by $4$.
Swarnava Bose
Swarnava Bose
asked
Aug 16, 2023
Combinatory
discrete-mathematics
permutation-and-combination
combinatory
+
–
767
views
1
answers
3
votes
Combinatorics Question uOttawa (University of Ottawa)
Consider the fourteen letters: $\text{A A A B B C C C C C D E E E}$ . An ARRANGEMENT is a sequence using $\text{all}$ ... order, somewhere in the arrangement). c) How many words have all letters distinct? d) How many arrangements have no two vowels consecutive?
Consider the fourteen letters: $\text{A A A B B C C C C C D E E E}$ .An ARRANGEMENT is a sequence using $\text{all}$ of these letters.For the purposes of this question, a...
Deepak Poonia
Deepak Poonia
asked
Jul 1, 2023
Combinatory
combinatory
discrete-mathematics
+
–
444
views
1
answers
0
votes
Byjus Workbook
Sir I am getting answer as 25 my approach k+1=3 k=2 n=12 nk+1=25 @sachinmittal1 @gate_cse
Sir I am getting answer as 25my approach k+1=3k=2n=12nk+1=25@sachinmittal1@gate_cse
JayRathi
JayRathi
asked
Jun 14, 2023
247
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0
answers
0
votes
Self doubt on Combinatorics Discrete Mathematics
What is the total number of integer partitions ( unordered Summation) of the natural number 8 ? I am getting 22. Is it correct ?
What is the total number of integer partitions ( unordered Summation) of the natural number 8 ?I am getting 22. Is it correct ?
Swarnava Bose
Swarnava Bose
asked
Jun 8, 2023
Combinatory
combinatory
discrete-mathematics
+
–
445
views
1
answers
0
votes
self doubt on Combinatory Discrete Mathematics
A power series expression has been converted to Partial Fractions to get :- $\frac{3}{1+5x} - \frac{2}{7-2x}+ \frac{5x}{3+2x} + \frac{7x}{5-2x}$ Find the Coefficient of $x^{n}$ where n represents natural number.
A power series expression has been converted to Partial Fractions to get :-$\frac{3}{1+5x} - \frac{2}{7-2x}+ \frac{5x}{3+2x} + \frac{7x}{5-2x}$Find the Coefficient of $x^...
Swarnava Bose
Swarnava Bose
asked
Jun 3, 2023
Combinatory
combinatory
discrete-mathematics
+
–
331
views
0
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0
votes
Let (1 + x)n = C0 + C1x + C2x2 + . . . + Cnxn, n being a positive integer. Then find the value of ( 1 + C0 C1 ) ( 1 + C1 C2 ) . . . ( 1 + Cn−1 Cn
JISAANNAGEORGE
JISAANNAGEORGE
asked
May 11, 2023
Combinatory
combinatory
+
–
216
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0
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0
votes
Clrs ex 5.2-2 chapter5 page133 4thedition
Hiring assistant. Initially assistant is NULL We have n candidates who hv come to interview for the position of assistant. Each candidate has distinct scores or level of qualifications. Now initially we have no assistant(stated earlier), so the first ... to solve this sum, and my answer is The best candidate comes in at kth position. Am I right? Thankyou.
Hiring assistant. Initially assistant is NULL We have n candidates who hv come to interview for the position of assistant. Each candidate has distinct scores or level of ...
yuyutsu
yuyutsu
asked
May 1, 2023
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