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

1 Answer
Oct 30, 2016

Answer:

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!