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

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(B) The word $ARRANGE$ contains $7$ letters: $A, A, R, R, N, G, E$. There are $2$ $A$'s,$2$ $R$'s,and $1$ each of $N, G, E$.The total number of arrang

Vedclass · Accepted Answer

$900$

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(B) The word $ARRANGE$ contains $7$ letters: $A, A, R, R, N, G, E$. There are $2$ $A$'s,$2$ $R$'s,and $1$ 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 come together,we treat $RR$ as a single unit. Now we have the letters ${RR}, A, A, N, G, E$,which is a total of $6$ units.The number of arrangements where $RR$ are together is $\frac{6!}{2!} = \frac{720}{2} = 360$.The number of arrangements where both $R$'s do not come together is the total arrangements minus the arrangements where they are together:$1260 - 360 = 900$.

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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