Question

Find number of words by using letters of word "ALLAHABAD"

Answer 1

There are $9$ letter in given word , in which $4A,2L$ and other are different .
So by taking all letters , number of different words are
$=\frac{\left(9\right)!}{\left(4\right)!\times \left(2\right)!}$
$=\frac{9\times 8\times 7\times 6\times 5\times \left(4\right)!}{\left(4\right)!\times 2\times 1}$
$=\frac{9\times 8\times 7\times 6\times 5}{2}$
$=7560$
hence number of words are $7560$.