assume that you have a bowl containing hard candies 50 cherr

assume that you have a bowl containing hard candies: 50 cherry, 50 strawberry, 40 orange, 70 lemon, and 40 pineapple. Assuming that the pieces of each flavor are identical, how many handfuls of 15 are possible with at least one piece of each flavor? (answer using combinatorics, please show how answer of 1001 is reached)

Solution

Number of toffees in Handful = 15

Number of varities of toffees = 5

Selecting one toffee of each variety = 15 - 5 = 10(toffees are left)

We can select 10 toffees from any 5 flavors

Using Beggar method, number of ways = C(n+r-1,r-1)

=> C(10+5-1,5-1)

=> C(14,4)

=> 14!/(10!4!)

=> (14 * 13 * 12 * 11)/24

=> 1001 ways