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:

Find the number of ways

Consider the given word $\text{ARRANGE}$

In the above word $\text{A}$ is repeated two times, $\text{R}$ is repeated two times, $\text{N}$, $\text{G}$ and $\text{E}$ are present in only one time.

The total number of possible arrangements can be expressed as,

$\frac{7!}{2!\times 2!}=\frac{7\times 6\times 5\times 4\times 3\times 2!}{2\times 1\times 2!}=1260$

Number of arrangements when two $\text{R}$ comes together can be expressed as,

$\frac{6!}{2!}=\frac{6\times 5\times 4\times 3\times 2!}{2!}=360$

Thus, the final answer for the number of ways which $\text{R}$ does not come together can be expressed as,

$1260-360=900$

Hence, the correct answer is Option B.