In a wholesale shop, there are three brands of pens.
- Brand A comes in packs of $5$.
- Brand B comes in packs of $4$.
- Brand C comes in packs of $3$
. A customer wants to buy $122$ pens from these three brands buying at least $1$ from each brand. The shopkeeper says that he will sell only in packs no loose pens will be sold. The customer bought $122$ pens in a total of $30$ packs and he bought from each brand, as specified. In how many ways (combinations) can the customer buy this?
