Question

The number of ways in which the letters of $"ARRANGE"$ be arranged so that
No two $R^{\prime }s$ comes together is

• A. $120$
• B. $900$
• C. $240$
• D. $360$

Answer 1

The correct option is B $900$

We have,

$"ARRANGE"$

$ARRANGE$

$\begin{array}{c}A\\ A\end{array}\begin{array}{c}R\\ R\end{array}\begin{array}{c}N\\ \end{array}\begin{array}{c}G\\ \end{array}\begin{array}{c}E\\ \end{array}$

$=\frac{7!}{2!2!}-\frac{6!}{2!}$

$=\frac{5040}{2\times 2}-\frac{720}{2}$

$=1260-360$

$=900$

Hence this is the answer,