SOLUTION: If the police have 7 suspects, how many different ways can they select 5 for a lineup?

Question 165380: If the police have 7 suspects, how many different ways can they select 5 for a lineup?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
If the police have 7 suspects, how many different ways can they select 5 for a lineup?
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Since it doesn't matter which order the suspects line up, it is a "combination" as opposed to a "permutation".
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Combination:
nCr = (n!)/[r!(n-r)!]
.
In our case:
n = 7
r = 5
.
nCr = (7!)/[5!(7-5)!]
nCr = (7!)/[5!(2)!]
nCr = (1*2*3*4*5*6*7)/[(1*2*3*4*5)(1*2)]
Canceling like-terms:
nCr = (6*7)/[(1*2)]
nCr = (42)/(2)
nCr = 21

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