14 Suppose that a bagel shop sells 5 different types of bage

14. Suppose that a bagel shop sells 5 different types of bagels, and you wish to purchase 15 bagels. How many different selections of 15 bagels can be made? (4 points)

Solution

Answer :

There are 5 kinds of bagels (n = 5), and we have to choose 15 bagels (r = 15).

In this problem, order doesn’t matter (combination) and repeats are okay (we assume that the shop won’t run out of any kind of bagels).

Therefore, there are C( n+r-1 , r) = C( 5+15-1,15) = C( 19,15) = 3876

hence, there are 3876 of  different selections of 15 bagels can be made.