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

1 Answer
Noah G
Jan 24, 2016

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!

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