Question

The number of ways in which the letters of the word $\text{"ARRANGE"}$ can be arranged such that both $\text{R}$ do not come together is?

• A. $360$
• B. $900$
• C. $1260$
• D. $1620$

Answer 1

The correct option is B

$900$

Explanation for the correct option(s)

Find the number of ways

Consider the given word $\text{"ARRANGE"}$,

We have $2$ repeating letters there are two $\text{R's}$ and two $\text{A's}$ and rest letters are one each.

Total possible number of ways is equal to $\frac{7!}{2!\times 2!}=\frac{7\times 6\times 5\times 4\times 3\times 2!}{2\times 1\times 2!}=1260$

Number of ways two $\text{R's}$ can be arranged together is given as $\frac{6!}{2!}=\frac{6\times 5\times 4\times 3\times 2!}{2!}=360$

Hence, the total number of ways when both $\text{R's}$ do not come together a re$1260-360=900$

Therefore, the correct answer is Option B.