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

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(B) The word $ARRANGE$ consists of $7$ letters: $A, A, R, R, N, G, E$. There are two $A$'s,two $R$'s,and one each of $N, G, E$. The total number of ar

Vedclass · Accepted Answer

$900$

Vedclass · Answer

(B) The word $ARRANGE$ consists of $7$ letters: $A, A, R, R, N, G, E$. There are two $A$'s,two $R$'s,and one each of $N, G, E$. The total number of arrangements is given by: $\frac{7!}{2! 	imes 2!} = \frac{5040}{4} = 1260$. To find the number of arrangements where both $R$'s are together,we treat the pair $(RR)$ as a single unit. Now we have $6$ units: $(RR), A, A, N, G, E$. The number of arrangements of these units is: $\frac{6!}{2!} = \frac{720}{2} = 360$. Therefore,the number of arrangements in which both $R$'s do not come together is: $1260 - 360 = 900$.

The number of ways in which the letters of the word $ARRANGE$ can be arranged such that both $R$ do not come together is

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