Answers

1. 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).

   Step-by-step explanation:

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2. Answer:

   The answer is 455 ways.

   Step-by-step 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

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