Question

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

Answer 1

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!