How does my professor come up with the recursive case in this algorithm analysis?

My professor gave us the following explanation for the recursive algorithm for finding the permutations of a set of numbers:

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When he has (T(m+1), n-1)) where does that come from? Why is it m+1 and n-1? I'm really confused as to where that comes from.

Solution

As he said, m represents the current size of P and n represents the size of S, in each recursive call you remove a number from S and add it to P, thus the size of your current permutation is increased by 1 (m+1) and the number of available numbers to add to the permutation is decreased by 1 (n-1)

Note that it is multiplied by n as you perform this action for each number in S.