Consider all possible permutations of the let | vedclass

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

Vedclass · Accepted Answer

$\frac{7!}{2!}$

Vedclass · Answer

(B) The word $EARTHQUAKE$ consists of $10$ letters: $E, A, R, T, H, Q, U, A, K, E$.The frequency of letters is: $E: 2, A: 2, R: 1, T: 1, H: 1, Q: 1, U: 1, K: 1$.To find the number of permutations containing the word $RAHU$,we treat the block $(RAHU)$ as a single unit.Now,the remaining letters are $E, E, A, T, Q, K$.Including the block $(RAHU)$,we have a total of $7$ items to arrange: $(RAHU), E, E, A, T, Q, K$.Among these $7$ items,the letter $E$ repeats $2$ times.The number of arrangements is given by the formula $\frac{n!}{p!}$,where $n=7$ and $p=2$ (for the two $E$'s).Thus,the number of permutations is $\frac{7!}{2!} = \frac{5040}{2} = 2520$.

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

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