SOLUTION: A school sent 5 students to a spelling bee.The team was made up of 4 people.How many different teams of 4 students could be sent?

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Question 127307: A school sent 5 students to a spelling bee.The team was made up of 4 people.How many different teams of 4 students could be sent?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Since order does not matter, we must use the combination formula:


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



5%21%2F%285-4%29%214%21 Plug in n=5 and r=4



5%21%2F1%214%21 Subtract 5-4 to get 1


Expand 5!
%285%2A4%2A3%2A2%2A1%29%2F1%214%21


Expand 1!
%285%2A4%2A3%2A2%2A1%29%2F%281%294%21



%285%2A4%2A3%2A2%2Across%281%29%29%2F%28cross%281%29%294%21 Cancel



%285%2A4%2A3%2A2%29%2F4%21 Simplify


Expand 4!
%285%2A4%2A3%2A2%29%2F%284%2A3%2A2%2A1%29



120%2F%284%2A3%2A2%2A1%29 Multiply 5*4*3*2 to get 120



120%2F24 Multiply 4*3*2*1 to get 24



5 Now divide



So 5 choose 4 (where order doesn't matter) yields 5 unique combinations