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Three of eight finalists will be selected and awarded $5,000

Three of eight finalists will be selected and awarded $5,000.00 scholarships. In how many ways can this selection be made?

Solution This solution is FREE courtesy of BrainMass!

Here the order of choice is not important. The problem is reduced to find how many combinations of 3 we can find out of a sample size =8.

There is a formula which allow us to calculate the combinations C:
C=n!/r!(n-r)!
Here: n!=8!=40320
r!=3!=6
(n-r)!=(8-3)!=5!=120.

So the number of available combinations of 3 out of 8 when the order is not important is:
C=40320/(6*120)=56 (ways)

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