1. ## Permutations and Combinations

Q. A box contains sweets of 6 different flavours. There are atleast 2 sweets of each flavour. A girl selects 3 sweets from the box. Given that these three sweets are not all of the same flavour, calculate the no. of different ways she can select her 3 sweets.

2. ## Re: Permutations and Combinations

Originally Posted by Ilsa
Q. A box contains sweets of 6 different flavours. There are atleast 2 sweets of each flavour. A girl selects 3 sweets from the box. Given that these three sweets are not all of the same flavour, calculate the no. of different ways she can select her 3 sweets. (Answer = 50)
There are $\binom{3+6-1}{3}=56$ ways to put three identical items into six different cells. But that means that some cell could have all the items. So if we require that no cell has all items the we must subtract 6.