SOLUTION: How many different words can be made out of the letters of the word ALLAHABAD? In how many of these with the vowels occupy the even places?

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Question 1105805: How many different words can be made out of the letters of the word ALLAHABAD? In how many of these with the vowels occupy the even places?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
How many different words can be made out of the letters of the word ALLAHABAD?
The answer would be 9! if the A's and also the L's were distinguishable.
But since the 4 A's are indistinguishable, we must divide by 4!.  Also 
since the 2 L's are indistinguishable, we must also divide by 2!.

Answer = 9%21%2F%284%212%21%29%22%22=%22%227560

In how many of these with the vowels occupy the even places?
They are all of the form _A_A_A_A_  where the 5 consonants B,H,D,L,L 
fill the blanks.

This number is the same as the number of distinguishable arrangements 
of consonants BHLLD, which is 5%21%2F2%21%22%22=%22%2260

Edwin