Question

The ice cream shop has 7 types of toppings available, and you decide to add 4 toppings to your bowl of 5 scoops of ice cream. How many combinations of 5 scoops of ice cream and 4 toppings are possible

Answer 1

Answer: 35

Step-by-step explanation:

The number of combinations of r things selected out of n things is given by

$^nC_r= \dfrac{n!}{r!(n-r)!}$

Given , the total number of types of toppings available = 7

The number of toppings needed to be selected = 4

Then, the number of ways to do this would be

$^7C_4=\dfrac{7!}{4!(7-4)!}\\\\=\dfrac{7\times6\times5\times4!}{4!3!}\\\\=\dfrac{7\times5}{1}=35$

Hence, the number of combinations of 5 scoops of ice cream and 4 toppings are possible = 35.