Question

find the number of permutations of the elements in the set {S,M,I,L,E}.

Answer 1

There are 120 permutations of all the letters in the set.

There are 24 permutations of a selections of 4. but, because there are 5 such combinations, there are 5*24=120 of these.

There are 6 permutations of a selection of 3 but, because there are 10 such combinations, there are 10*6=60 of these.

There are 2 permutations of a selection of 2 but, because there are 10 such combinations, there are 10*2=20 of these.

The total number of permutations is therefore 120+120+60+20=320.