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 ?

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- Apr 25th 2009, 04:48 PMsleepywalkerNumber 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 ? - Apr 25th 2009, 05:28 PMSoroban
Hello, sleepywalker!

Quote:

How many arrangements are there of two A's, one E, one I and seven X's

in which no two vowels are adjacent ?

. . _ 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: .$\displaystyle 8\cdot7\cdot6\cdot5 \:=\:1680$ ways.

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

- Apr 25th 2009, 05:35 PMsleepywalker
(Clapping)

I think this is the right answer.

thank you so much for your time.