SOLUTION: how many ways can 15 players be chosen to form a baseball team of 9?

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Question 151513: how many ways can 15 players be chosen to form a baseball team of 9?
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!


Since order does matter, we must use the permutation formula:




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



15%21%2F%2815-9%29%21 Plug in n=15 and r=9



15%21%2F6%21 Subtract 15-9 to get 6



Expand 15!
%2815%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F6%21



Expand 6!
%2815%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%286%2A5%2A4%2A3%2A2%2A1%29



%2815%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2Across%286%2A5%2A4%2A3%2A2%2A1%29%29%2F%28cross%286%2A5%2A4%2A3%2A2%2A1%29%29 Cancel



15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7 Simplify




1816214400 Now multiply 15*14*13*12*11*10*9*8*7 to get 1,816,214,400


So 15 choose 9 (where order does matter) yields 1,816,214,400 unique combinations