Question

If all the letters of the word '$RANDOM$' are arranged in all possible ways, then the probability that no letter is in its original position is

• A. $\frac{265}{720}$
• B. $\frac{1}{720}$
• C. $\frac{6P_6}{720}$
• D. $\frac{1}{6}$

Answer 1

The correct option is A $\frac{265}{720}$

The total number of possible outcome $=6!=720$
We will calculate the total number of favourable outcome by derangement formula
$=6!\times \{\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!}+\frac{1}{6!}\}=265$
Hence, the probability$=\frac{265}{720}$