An amusement park has 13 roller coasters. In how many ways can you choose 4 of the roller coasters to ride during your visit to the park?

1 Answer
Sep 30, 2016

Assuming you want to choose 4 different roller coasters.

Explanation:

Then for the first you choose from all 13, for the second from the remaining 12, etc.

This gives you #13xx12xx11xx10=17160# ways.

But then, if the order in which you ride them doesn't matter, you have to divide this by the number of possible orders in which to ride your 4 choices: #4xx3xx2xx1=24#

Summary :
For choosing 4 rides out of 13, when order is unimportant:
#N=17160/24=715#

Note: If you use a GC, the function #nCr# is used:
#13nCr4=715#