Question

An ice cream shop has 15 different toppings for sundaes, and it is running a special for 3 free toppings. How many 3-topping sundaes can be made, assuming all 3 toppings chosen are different?
A.
182
B.
455
C.
1,365
D.
2,730

Answer 1

Answer:

B. 455

Step-by-step explanation:

The order in which the toppings are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

3 toppings from a set of 15. So

$C_{15,3} = \frac{15!}{3!(15-3)!} = 455$

455 3-topping sundaes can be made.