Problem 3


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.]


Solution 1:


There are three non-overlapping possibilities:


Case I: two Ps, one E, one S. This has or 12 words.

Case II: one P, two Es, one S. This has or 12 words.

Case III: two Ps, two E, no S. This has or 6 words.

Total = 12 + 12 + 6 = 30



Solution 2:


There are ways to arrange all letters if no two were the same; dividing by repetitions: 2! and 2! we have 120/4 = 30.


Solution 3:


An organized student may list them, there are only 30.