Question

If four letters are placed into 4 addressed envelopes at random, the probability that exactly two letters will go wrong is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. 0

Answer 1

The correct option is C $\frac{1}{4}$

Total ways $=4!$
$2$ are placed correct and other two wrong, no. of ways of doing this $=$ no. of ways of choosing

two letter which are misplaced ${=}^4{C}_2$

And there is only one way in which both of them are wrongly placed
$\Rightarrow P{=}^4{C}_2/4!=1/4$