(B) The word $CALCUTTA$ contains $8$ letters in total.The frequency of each letter is: $C: 2, A: 2, L: 1, U: 2, T: 2$.The number of distinct arrangeme

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(B) The word $CALCUTTA$ contains $8$ letters in total.The frequency of each letter is: $C: 2, A: 2, L: 1, U: 2, T: 2$.The number of distinct arrangements is given by the formula $\frac{n!}{n_1! n_2! n_3! ... n_k!}$.Here,$n = 8$,and the repetitions are $C=2, A=2, U=2, T=2$.Required number of arrangements $= \frac{8!}{2! 2! 2! 2!} = \frac{40320}{2 \times 2 \times 2 \times 2} = \frac{40320}{16} = 5040$.

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 distinct arrangements of the letters of the word $CALCUTTA$.

A
$2520$
B
$5040$
C
$10080$
D
$40320$

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

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Find the number of distinct arrangements of the letters of the word $CALCUTTA$.

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