Question

Find the number of permutations of the letters of the word $\text{ALLAHABAD.}$

Answer 1

Finding number of permutations of the word $\text{ALLAHABAD.}$
In $\text{ALLAHABAD.}$
$4A,2L,1H,1B$ and $1D$

So, by using formula$=\frac{n!}{P_1!P_2!}$(When repeating)

Here, $n=9,P_1=4,P_2=2$

$\therefore$ Total number of Permutation $=\frac{n!}{P_1!P_2!}=\frac{9!}{4!2!}=\frac{9\times 8\times 7\times 6\times 5\times 4!}{4!\times 2\times 1}=\frac{9\times 8\times 7\times 6\times 5}{2}=7560$