Question

Perfect Pizza has 15 toppings listed on their menu. How many ways could a customer choose a pizza that contains 3 different toppings?

Answer 1

The answer is 455 ways.

Explanation:

If adding only twelve, you must leave out three of the fifteen, and the number of ways is = 15! / (3! * 12!).

1∗2∗3∗4∗5∗6∗6∗8∗9∗10∗11∗12∗13∗14∗15 over

(1∗2∗3)∗(1∗2∗3∗4∗5∗6∗6∗8∗9∗10∗11∗12) =

13∗14∗15 over

(1∗2∗3)

27306 = 455

Answer 2

Answer: If all toppings are distinct, then you have C 4 15 combinations. If there are three distinct toppings, you have 3 ⋅ C 3 15 combinations (because we have C 3 15 choices for toppings and then 3 choices for which of those three toppings is doubled).

Explanation: