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. Using the formula nCr - n!/ r!(n-r)!
To find the number of different combinations of machines that Geoff can choose from, we need to use the formula for combinations, which is given by nCr, where n is the total number of machines and r is the number of machines Geoff chooses to use.
In this case, n = 11 (since there are 11 different types of machines in the weight room), and r = 3 (since Geoff has time to use only 3 machines).
The formula for combinations is nCr = n! / (r!(n-r)!)
Using this formula, we can calculate the number of combinations:
11! / (3!(11-3)!)
= 11! / (3!8!)
= (11 * 10 * 9 * 8!)/(3! * 8!)
= (11 * 10 * 9) / (3 * 2 * 1)
= 990 / 6
= 165
So, Geoff can choose from 165 different combinations of machines to use.