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!
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.