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.
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)!
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