# Math Help - Number of arrangements

1. ## Number of arrangements

Hey guys, I'm not sur how to solve this question:
how many arrangements are there of there of two a's, one e, one i and seven x's in which no two vowels are adjacent ?
I found that the answer would be 3! * 10! / (5! * 2!)
is that correct ?

2. Hello, sleepywalker!

How many arrangements are there of two A's, one E, one I and seven X's
in which no two vowels are adjacent ?
Place the seven X's in a row, inserting spaces before, after, and between them.

. . _ X _ X _ X _ X _ X _ X _ X _

Now we place the 4 vowels in the 8 spaces.

If we had 4 different vowels, there would be: . $8\cdot7\cdot6\cdot5 \:=\:1680$ ways.

Since the two A's are identical, there are: . $\frac{1680}{2} \:=\:840$ arrangements.

3. I think this is the right answer.
thank you so much for your time.