(A) The word $ALLAHABAD$ contains $9$ letters in total.These letters are: $A, L, L, A, H, A, B, A, D$.The frequency of each letter is:$A: 4$$L: 2$$H:

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(A) The word $ALLAHABAD$ contains $9$ letters in total.These letters are: $A, L, L, A, H, A, B, A, D$.The frequency of each letter is:$A: 4$$L: 2$$H: 1$$B: 1$$D: 1$Using the formula for permutations of a multiset,the number of arrangements is given by $\frac{n!}{n_1! n_2! ... n_k!}$.Here,$n = 9$,$n_1 = 4$ (for $A$),and $n_2 = 2$ (for $L$).Number of permutations $= \frac{9!}{4! 2!} = \frac{362880}{24 \times 2} = \frac{362880}{48} = 7560$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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Find the number of permutations of the letters of the word $ALLAHABAD$.

A
$7560$
B
$3780$
C
$15120$
D
$30240$

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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Find the number of permutations of the letters of the word $ALLAHABAD$.

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