SOLUTION: How many different seating arrangements are possible for 6 people in 4 chairs?

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Question 166109: How many different seating arrangements are possible for 6 people in 4 chairs?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Since order does not matter (ie the seats have no unique positions), we must use the combination formula:


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



6%21%2F%286-4%29%214%21 Plug in n=6 and r=4



6%21%2F2%214%21 Subtract 6-4 to get 2


Expand 6!
%286%2A5%2A4%2A3%2A2%2A1%29%2F2%214%21


Expand 2!
%286%2A5%2A4%2A3%2A2%2A1%29%2F%282%2A1%294%21



%286%2A5%2A4%2A3%2Across%282%2A1%29%29%2F%28cross%282%2A1%29%294%21 Cancel



%286%2A5%2A4%2A3%29%2F4%21 Simplify


Expand 4!
%286%2A5%2A4%2A3%29%2F%284%2A3%2A2%2A1%29



360%2F%284%2A3%2A2%2A1%29 Multiply 6*5*4*3 to get 360



360%2F24 Multiply 4*3*2*1 to get 24



15 Now divide



So 6 choose 4 (where order doesn't matter) yields 15 unique combinations. So there are 15 possible ways that 6 people can sit in 4 chairs.