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: 455 (plato/edmentum).

Answer 2

B. 455

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) = (n!)/(x!(n-x)!)`

In this question:

3 toppings from a set of 15. So

`C_(15,3) = (15!)/(3!(15-3)!) = 455`

455 3-topping sundaes can be made.