In how many different ways can the letters of | vedclass

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Question

(A) The word $ALLAHABAD$ contains a total of $9$ letters.In this word,the letter $A$ appears $4$ times,the letter $L$ appears $2$ times,and the letter

Vedclass · Accepted Answer

$7560$

Vedclass · Answer

(A) The word $ALLAHABAD$ contains a total of $9$ letters.In this word,the letter $A$ appears $4$ times,the letter $L$ appears $2$ times,and the letters $H, B, D$ each appear once.Therefore,the required number of permutations is given by the formula for permutations of a multiset:$	ext{Number of permutations} = \frac{n!}{n_1! n_2! ... n_k!}$Substituting the values: $\frac{9!}{4! 2! 1! 1! 1!} = \frac{9 	imes 8 	imes 7 	imes 6 	imes 5 	imes 4!}{4! 	imes 2 	imes 1 	imes 1 	imes 1}$$= \frac{9 	imes 8 	imes 7 	imes 6 	imes 5}{2} = 9 	imes 8 	imes 7 	imes 3 	imes 5 = 7560$.

In how many different ways can the letters of the word $ALLAHABAD$ be permuted?

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