Question

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

• A. $\frac{7!}{2!2!}$
• B. $\frac{7!}{2!}$
• C. $\frac{6!}{2!}$
• D. $5!\times 2!$

Answer 1

The correct option is C

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

The letters of the words $ARRANGE$ can be written as
$AAEGNRR$
Considering $R$'s to be together always, then there will be $6$ letters (objects) with two identical objects $($two $A$'s$)$. These can be arranged in $\frac{6!}{2!}$ ways.