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

Respuesta :

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:

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

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

3 toppings from a set of 15. So

[tex]C_{15,3} = \frac{15!}{3!(15-3)!} = 455[/tex]

455 3-topping sundaes can be made.

answer: 455 (plato/edmentum).

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