# How many different arrangements can be made using all of the letters in the word REARRANGE?

##### 1 Answer
Oct 30, 2016

There are $15 , 120$ ways.

#### Explanation:

For problems, like these, we need to consider the number of total letters and the number of repeated letters.

There are 9 letters in this word, so if all the letters were different there would be 9! ways of arranging them.

However, we have $3$ R's, $2$ A's and $2$ E's.

So, this expression becomes (9!)/(3! xx 2! xx 2!) = (362,280)/(6 xx 2 xx 2) = (362,280)/24 = 15,120.

Hopefully this helps!