Hello, Punch!

In this question, a 'word' is defined to be any set of letters in a row,

whether of not it makes sense. . Find how many different 'words'

can be made using only 5 letters of the word SYLLABUS.

I tried to separate them into 4 cases,

1) all different letters

2) two S's

3) two L's

4) two S's and two L's

An excellent game plan! How far did you get?

We have 8 letters, 6 distinct: .

1) Five different letters

. . Choose 5 of the 6 letters and permutate them:.

2) Two S's: .

. . Choose 3 of the other 5 letters:.

. . and permute the 5 letters:.

3) Two L's:.

. . Choose 3 of the other 5 letters:.

. . and permutate the 5 letters:.

4) Two S's, two L's:.

. . Choose 1 of the other 4 letters:.

. . and permutate the 5 letters:.

There are:. "words".