The number of ways in which the letters of th | vedclass

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(C) The word is $ARRANGE$. It contains $7$ letters: $A(2), R(2), N(1), G(1), E(1)$.To ensure the two $R$'s occur together, we treat the block $(RR)$ a

Vedclass · Accepted Answer

$\frac{6!}{2!}$

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(C) The word is $ARRANGE$. It contains $7$ letters: $A(2), R(2), N(1), G(1), E(1)$.To ensure the two $R$'s occur together, we treat the block $(RR)$ as a single unit.Now, the letters to be arranged are $(RR), A, A, N, G, E$. This gives us $6$ units in total.Among these $6$ units, the letter $A$ repeats $2$ times.The number of ways to arrange these $6$ units is $\frac{6!}{2!}$.Within the block $(RR)$, the two $R$'s can be arranged in $\frac{2!}{2!} = 1$ way.Therefore, the total number of permutations is $\frac{6!}{2!} 	imes 1 = \frac{6!}{2!}$.

The number of ways in which the letters of the word $ARRANGE$ can be permuted such that the $R$'s occur together is:

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