SOLUTION: There are 15 people waiting to take their driver's training test. In how many ways can the 15 be divided equally among 3 examiners? I know this is probably a combination problem

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Question 883683: There are 15 people waiting to take their driver's training test. In how many ways can the 15 be divided equally among 3 examiners?
I know this is probably a combination problem so can you show me using the long way and the calculator?
Answer by pj66(7) (Show Source):
You can put this solution on YOUR website!
The questions says we need to divide equally among 3 examiners. We will use combination formula - (n)C_r = (n!)/(r!*(n-r)!)
15 people are to be divided amongst 3 examiners i.e 5 people for each examiner.
for first examiner : (15)C_5 = 3036 ---------(1)
Because the first one can choose any five from pool of fifteen.
for second examiner : (10)C_5 = 252 ---------(2)
Because second examiner will have to choose 5 people from remaining 15.
for third examiner : (5)C_5 = 120 ---------(3)
Because third examiner will have the last five.
Number of ways in which 15 people can be chosen by 3 examiners we will multiply (1),(2) and (3) = 91808640
Let me know if you have any doubts and whether the answer is correct.