Question

An amusement park has 15 roller coasters. In how many ways can you choose 10 of the roller coasters to ride during your visit to the park? *

Answer 1

3003 ways

Explanation:

We are in a combination or permutation exercise, the difference between them is if the order matters (permutations) or does not matter (combinations),

in this case the order does not matter, since they only ask us for the ways to choose 10 of 15 roller coasters, therefore it would be a combination:

nCr = n! / (r! * (n-r)!

we know that n = 15 and r = 10, we replace:

15C10 = 15! / (10! * (15-10)!

15C10 = 3003

In other words, there are 3003 ways to choose 10 of the 15.