How may permutations of the word "spell" are there?

1 Answer
Jul 27, 2017

60 Permutation


In general, to find the number of permutations available using a certain amount of unique numbers, letters, or entities, you would take the number of unique entities, lets say 5, and make it a factorial. If we were to find the number of permutations available with the word MATH, we would find 4!, or 24 permutations of the word.

Now in the case of the word SPELL, there are 2 repeating letters, the two L's. The problem comes with unique solutions. Lets rename the word SPELl, with one L being uppercase and one being lowercase. There would be a difference if this was the case with these two permutations.

  1. SElPL
  2. SELPl

But if both letters are capital, then there would be no difference in the permutations. Therefore we can take our original rule, of taking 5! to figure out the number of permutations, and divide by 2, to get:

5!/2 = 120/2 = 60.