SOLUTION: there are 4 positions with 6 people to fill. How many different ways can the officers be elected?

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Question 90525: there are 4 positions with 6 people to fill. How many different ways can the officers be elected?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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




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



6%21%2F%286-4%29%21 Plug in n=6 and r=4



6%21%2F2%21 Subtract 6-4 to get 2



Expand 6!
%286%2A5%2A4%2A3%2A2%2A1%29%2F2%21



Expand 2!
%286%2A5%2A4%2A3%2A2%2A1%29%2F%282%2A1%29



%286%2A5%2A4%2A3%2Across%282%2A1%29%29%2F%28cross%282%2A1%29%29 Cancel



6%2A5%2A4%2A3 Simplify




360 Now multiply 6*5*4*3 to get 360


So 6 choose 4 (where order does matter) yields 360 unique combinations