Question

How do you solve this problem?

Say Matt is interested in riding only roller coasters, but he has only enough time to ride 12 of the 16 roller coasters at Cedar Point. How many combinations of 12 roller coasters are there, assuming Matt wouldn’t ride any roller coaster multiple times?

Answer 1

1820

Explanation:

Since the order of the rides is not important, and repeats are not allowed, the number of combinations can be calculated using the formula:

`_(n)C_(r) =(n!)/(r!(n-r)!)`

where n is the number objects (in this case, 16) and r is the number of samples (in this case, 12).

`_(16)C_(12) =(16!)/(12!(16-12)!)\\_(16)C_(12) =(16!)/(12!4!)\\_(16)C_(12) =1820`