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

Jan 24, 2016

#### Answer:

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:

= $\frac{24}{2}$

= 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!