SOLUTION: From a club of 25 members, how many ways can a president, vice-president, secretary, and treasurer be selected? which formula is used and does n=25 and r=4?

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Question 149387: From a club of 25 members, how many ways can a president, vice-president, secretary, and treasurer be selected?
which formula is used and does n=25 and r=4?
Answer by jim_thompson5910(21677) 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



25%21%2F%2825-4%29%21 Plug in n=25 and r=4



25%21%2F21%21 Subtract 25-4 to get 21



Expand 25!
%2825%2A24%2A23%2A22%2A21%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F21%21



Expand 21!
%2825%2A24%2A23%2A22%2A21%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%2821%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29



%2825%2A24%2A23%2A22%2Across%2821%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%29%2F%28cross%2821%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%29 Cancel like terms.



25%2A24%2A23%2A22 Simplify




303600 Now multiply 25*24*23*22 to get 303,600


So 25 choose 4 (where order does matter) yields 303,600 unique combinations