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4! (Because E is repeated so we just take 1) P,E,L,S (4 letters) So they can be arranged 4!=24

24

Another way:

 

SLEEP has 5 letters. 5! / 2! =60 permutations. Or 60 / 5 letters =12 for each letter. Since we have 2 of the same letter, then 2 x 12 = 24.

Let's assume that the letter starts with E, because that's what we're looking for.

 

There are four other letters, S, L, E, and P.

Since none of them are the same letter, we can simply do 4! and get 24.

 

NOTE:

Let's say the word was SEEEP.

Then the letters would be S, E, E, and P.

This would make 4!/2!, because we are repeating E twice.

 

You are very welcome!

:P