Thread: Counting problem

If Set S = {1,2,3,4}, how many permutations of are there so that no subset is ever followed by a subset of smaller size?

So this is what I did:

Possible sizes are 0, 1, 2, 3, 4


which is 1, 4, 6, 4, 1, respectively

So I choose smallest first, which is still in respective order, so:

I did 1! * 4! * 6! * 4! * 1! which came out to be 414720

However, I doubt this is right. Anyone know if I did anything wrong?

Thanks.

I assume you mean permutations of (the set of all subsets of S)

What you did was indeed correct. Not very surprising, considering the total amount of permutations of is 16!

Yeah whoops that's what I meant. I wasn't sure if this was correct because it seemed too easy for an assignment question. Anyways, thanks for the help!