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?

Question

Casey Phillips

Mathematics

5 February, 03:37

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?

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Answers (1)

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Conway · Answer 1

455

Step-by-step explanation:

This is a combination problem: we need to create groups of 3 elements from the pool of 15 options, and the order of the elements in the group doesn't matter.

So, to solve the problem, we need to find the combination of 15 choose 3:

C (15,3) = 15! / (3! * 12!) = (15*14*13) / (3*2) = 455

We can make 455 different 3-topping sundaes.