Question:
How many different words can be formed by using all the letters of the word ‘ALLAHABAD’?
Solution:
Given: We have 9 letters
To Find: Number of words formed with Letter of the word 'ALLAHABAD.'
The formula used: The number of permutations of $n$ objects, where $p_{1}$ objects are of one kind, $p_{2}$ are of the second kind, ..., $p_{k}$ is of a $k^{\text {th }}$ kind and the rest if any, are of a
different kind is $=\frac{n !}{p_{1} ! p_{2} ! \ldots \ldots \ldots \ldots p_{k} !}$
‘ALLAHABAD’ consist of 9 letters out of which we have 4 A’s and 2 L’s.
Using the above formula
Where,
$n=9$
$p_{1}=4$
$p_{2}=2$
$\Rightarrow \frac{9 !}{4 ! 2 !}=7560$
7560 different words can be formed by using all the letters of the word ‘ALLAHABAD.’