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 p1 objects are of one kind, p2 are of the second kind, ..., pk is of a kth kind and the rest if any, are of a different kind is = \(\frac{n!}{p_1!p_2! .....p_k!}\)
‘ALLAHABAD’ consist of 9 letters out of which we have 4 A’s and 2 L’s.
Using the above formula
Where,
n = 9
p1 = 4
p2 = 2
\(\frac{9!}{4!2!}\) = 7560
7560 different words can be formed by using all the letters of the word ‘ALLAHABAD.’
