Question 1105805
How many different words can be made out of the letters of the word ALLAHABAD?
<pre>
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!/(4!2!)}}}{{{""=""}}}{{{7560}}}
</pre>
In how many of these with the vowels occupy the even places? 
<pre>
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!/2!}}}{{{""=""}}}{{{60}}}

Edwin</pre>