SOLUTION: How many ways can a committe of 7 people be selected from a group of 15 people

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Question 106757: How many ways can a committe of 7 people be selected from a group of 15 people
Answer by jim_thompson5910(28595) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that order does matter.

Since order matters, we must use the permutation formula:




n%21%2F%28n-r%29%21 Start with the given formula



15%21%2F%2815-7%29%21 Plug in n=15 and r=7



15%21%2F8%21 Subtract 15-7 to get 8



Expand 15!
%2815%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F8%21



Expand 8!




Cancel



15%2A14%2A13%2A12%2A11%2A10%2A9 Simplify




32432400 Now multiply 15*14*13*12*11*10*9 to get 32,432,400


So 15 choose 7 (where order does matter) yields 32,432,400 unique combinations