(B) The word $EARTHQUAKE$ consists of $10$ letters: $E, A, R, T, H, Q, U, A, K, E$. The frequencies are: $E: 2, A: 2, R: 1, T: 1, H: 1, Q: 1, U: 1, K:

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(B) The word $EARTHQUAKE$ consists of $10$ letters: $E, A, R, T, H, Q, U, A, K, E$. The frequencies are: $E: 2, A: 2, R: 1, T: 1, H: 1, Q: 1, U: 1, K: 1$. To find the number of permutations containing the block $RAHU$,we treat $RAHU$ as a single unit. Now,the items to be arranged are: ${RAHU}, E, A, T, Q, K, E$. There are $7$ items in total,where $E$ repeats $2$ times. The number of arrangements is given by $\frac{7!}{2!}$. Thus,the correct option is $B$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Consider all possible permutations of the letters of the word $EARTHQUAKE$. The number of permutations containing the word $RAHU$ is:

A
$\frac{7!}{2!2!}$
B
$\frac{7!}{2!}$
C
$7!$
D
None of these

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

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Consider all possible permutations of the letters of the word $EARTHQUAKE$. The number of permutations containing the word $RAHU$ is:

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