Question

How many four–letter permutations can be formed from the letters of the word OHIO?

Answer 1

Since two letters are the same, you will divide n!, or the total number of letters in the word, by `n_1!(n_2!)`, etcetera, where `n_1` is the number of repeated letters in the word, and `n_2!` is another type of repeated letter, such as in the word ANNA, `n_1!` = 2! and `n_2!` = 2!, because there are 2 a's and 2 n's.

Explanation:

number of different words possible = `(4!)/(2!)`, since there are two o's in Ohio and therefore two repeated letters

When calculated:

= `24/2`

= 12

So, 12 four word permutations are possible with the letters in the word Ohio.

Exercises:

1. Find the number of combinations of the letters in the word CIVIC

2. Find the number of combinations of the letters in the word PINEAPPLE

Hopefully you understand!