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.

(Answer = 50)

Re: Permutations and Combinations

Quote:

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)

That answer is correct.

There are $\displaystyle \binom{3+6-1}{3}=56$ 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.