The gym has 11 different types of machines in the weight room. Geoff has time to use only 3 of them this afternoon. How many different combinations of machines can Geoff choose from to use? Show your work or explain how you got your answer.
To find the number of different combinations of machines that Geoff can choose from, we can use the combination formula.
The combination formula is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of items and r is the number of items we want to choose.
In this case, Geoff wants to choose 3 machines out of a total of 11 machines.
Using the combination formula:
C(11, 3) = 11! / (3!(11-3)!)
= 11! / (3!8!)
= (11 * 10 * 9) / (3 * 2 * 1)
= 165
Therefore, Geoff can choose from 165 different combinations of machines.