Question

The ice cream shop offers 31 flavors. you order a double scoop cone how many different ways can the clerk put the ice cream on the cone if you want two different flavors​

Answer 1

Answer:

465

Step-by-step explanation:

Since we are looking for the the number of combinations to have 2 different flavors in the ice cream, we can use the formula for combination.

$_{n}C_{k}=\dfrac{n!}{k!(n-k)!}$

Our variables are:

n = 31

k = 2

$_{31}C_{2}=\dfrac{31!}{2!(31-2)!}$

$_{31}C_{2}=\dfrac{31!}{2!29!}$

$_{31}C_{2}=\dfrac{31!}{2!29!}$

$_{31}C_{2}=465$

The number of possible combinations of having 2 different flavors out of 31 different flavors is 465.