assume you have a bowl containing hard candies 50 cherry 50

assume you have a bowl containing hard candies: 50 cherry, 50 strawberry, 40 orange, 70 lemon, and 40 pineapple. assuming the pieces of each flavor are identical, how many handfuls of 15 are possible with at least one piece of each flavor?

Solution

First we have to select a piece from  50 cherry,a piece from 50 strawberry,a piece from 40 orange,a piece from 70 lemon, anda piece from 40 pineapple

number of ways=50*50*40*70*40 =280000000

Now we have to select remaining 10 pieces from remaining 245 pieces

number of ways = 245C₅

al number of ways=280000000*245C₅