How many 4-letter “words” may be formed form the letters PEEPS? For example PEEP, PPEE, SPPE, etc.
[Problem submitted by Don Hentschel, LACC Assistant Professor of Mathematics.]
There are three non-overlapping possibilities:
Case I: two P’s, one E, one S. This has or 12 words.
Case II: one P, two E’s, one S. This has or 12 words.
Case III: two P’s, two E, no S. This has or 6 words.
Total = 12 + 12 + 6 = 30
There are ways to arrange all letters if no two were the same; dividing by repetitions: 2! and 2! we have 120/4 = 30.
An organized student may list them, there are only 30.