1. ## Permutations and combinations?

A set of triplets and two pairs of twins are posing for a photo-taking session. How
many different ways are there to arrange them in a row if the siblings are to stand next to each other?

I was thinking the answer would be 3! * 2! * 2! = 24 but its not,the answer is 144.
What am I doing wrong?

2. Originally Posted by mngeow
A set of triplets and two pairs of twins are posing for a photo-taking session. How
many different ways are there to arrange them in a row if the siblings are to stand next to each other?

I was thinking the answer would be 3! * 2! * 2! = 24 but its not,the answer is 144.
What am I doing wrong?
I think the info that they are triplets/twins is somewhat strange, since there is a possibility that they are so-called identical triplets/twins, and thus could be considered in some sense non-distinguishable for counting purposes.

Nevertheless the given answer indicates that we do in fact view the siblings as distinct people, so:

Treat each set of siblings as a single unit, there are three such units, giving 3!

For the triplet, there are 3! ways to arrange them among themselves

For each pair of twins, there are 2! ways to arrange them among themselves

Thus overall we get 3! * 3! * 2! * 2! = 144.

3. Oh I see where i went wrong now.Thanks alot