# 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(28717)   (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: Start with the combination formula. Plug in and Subtract to get 2 Expand 6! Expand 2! Cancel Simplify Expand 4! Multiply 6*5*4*3 to get 360 Multiply 4*3*2*1 to get 24 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.