In how many can a group of 18 children be split into 3 groups of equal size? (The names of the groups isn't important, only who is with who).

Is this the correct answer:

We'll line the kids up in a line. There are 18! ways to do this.

The first 6 kids are group 1, the 2nd 6 are group 2 and the 3rd 6 are group 3.

We'll divide 18! by 3! because all that matters is whom is whom and not the name of the group.

We'll divide this number by 6! because the group ABCDEF is the same as BACDEF.

So in total we have 18!/(3!*6!) ways of splitting up the kids. Is this correct?

Thank you