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Syllabus: Combinatorics: Counting, Recurrence relations, Generating functions.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2024-1} & \textbf{2024-2} & \textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &0&0&1& 1&1&0&0&0.5&1
\\\hline\textbf{2 Marks Count} &0&0&1& 2 &0&1&0&0.67&2
\\\hline\textbf{Total Marks} & 0&0&3&5 &1&2&0&1.83&5\\\hline
\end{array}}}$$

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#22
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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 ...
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#23
193
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1 answers
2 votes
GO Classes 2024 | IIITH Mock Test 5 | Question: 39
The minimum number of integers to be selected from the set $S = \{1, 2, \dots , 9\}$ so that the difference of at least two of the integers is guaranteed to be $5$ is ___...
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#24
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Flamingos Fanny and Freddy have three offspring: Happy, Glee, and Joy. These five flamingos are to be distributed to seven different zoos so that no zoo gets both a parent and a child :(. It is not required that every zoo gets a flamingo. In how many different ways can this be done? here if i am using case method on children i am getting a different answer than when i am using case methon on parents, why is that?
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#25
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2 answers
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GO Classes 2023 | IIITH Mock Test 1 | Question: 4
How many ways are there to arrange the $12$ letters of $\text{AAABBBBCCCCC}$ without having two $\text{Cs}$ together?$2652$$1960$$1826$$2260$
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#26
906
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1 answers
3 votes
GO Classes 2023 | IIITH Mock Test 1 | Question: 33
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ where $a_n = \binom {n+4}{n}$ for $n= 0,1,2,\ldots ?$$\frac{1...
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#27
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kenneth rosen, counting, exercise: 6.5, question: 50
How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?
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#28
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Kenneth Rosen, exercise: 6.2, question: 8
Show that if f is a function from S to T , where S and T are finite sets with |S| |T |, then there are elements s1 and s2 in S such that f (s1) = f (s2), or in other wor...
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#29
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Can any one solve this , 6B and 4G ,at least 2 girls should be together in circular arrangement
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#30
759
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1 answers
4 votes
TIFR CSE 2023 | Part A | Question: 2
How many distinct rectangles can be formed using the vertices in the grid shown below? Squares are also counted as rectangles, and two rectangles are distinct if either t...
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#31
556
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3 votes
TIFR CSE 2023 | Part A | Question: 12
Suppose is a piece on a chess board that attacks squares that are exactly two steps in the vertical direction, and squares that are adjacent horizontally (as marked with...
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#32
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Kenneth Rosen, exercise 6.1, Qs - 42 (d)
How many 4-element DNA sequences contain exactly three of the four bases A, T, C, and G?Solution given: There are four ways to choose which letter is to occur twice and t...
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#33
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#Combinatorics #Self doubt
How many 3 digits number are there which are divisible by 3 and repetition of digits NOT allowed.?
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#34
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4 answers
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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 $L_{2}=3$.Which one of t...
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#35
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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|...
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#36
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GATE CSE 2023 | Memory Based Question: 15
The Lucas sequence $L_n$ is defined by the recurrence relation:$L_n=L_{n-1}+L_{n-2}$, for $n \geq 3$ with $L_1=1$ and $L_2=3$.Which one of the options given is TRUE?$L_n=...
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#37
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GATE CSE 2023 | Memory Based Question: 16
How many permutations of $U$ separate $A$ from $B?$$2\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2 k) !(k!)^2$$\left(\begin{array}{c}n \\ 2 k\end{array}\right)(n-2...
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#38
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#Combinatorics and Counting # Permutations and Combinations
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#39
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#selfdoubt
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#40
1.8k
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1 answers
22 votes
Recurrence Relation - Self Doubt
What is the recurrence relation for the ternary strings of length $n$ which can be constructed using 0,1 or 2 only such that the number of 0’s and number of 1's is od...
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