How to use combination in this question

Question

In how many ways can n people be divided into 2 equal groups or 3 equal groups (given that n is a factor of 6)

I don't know how to utilize combination to solve this problem, as it is about splitting people into groups instead of finding how many possibilities to form a group.

Can someone explain how to use the combination rule to solve this problem with dividing people into groups?

They are indistinguishable so combination rather than permutations — nabu1227, May 30 '17 at 03:14

score 0 · Accepted Answer · answered May 28 '17 at 07:52

0

To divide a group of n people into two, you pick $\frac{n}{2}$ people from the group. This can be done in $\binom{n}{n/2}$ ways. You can find the number of ways to divide them into 3 groups following the same logic.

answered May 28 '17 at 07:52

Hikaru

941

So for groups of 3 it is $\binom{n}{n/3}$ and so on? – nabu1227 May 28 '17 at 08:55
Yes. It is important that 3 and 2 divide n, otherwise $ \binom {n}{n/2} $ and $ \binom {n}{n/3} $ will be meaningless. – Hikaru May 28 '17 at 09:08

How to use combination in this question

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