Question

There are $6$ letters and $6$ directed envelopes. Find the number of ways in which all letters are put in the wrong envelopes.

Answer 1

Answer: 265.00

$D_6=6!\left[\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!}+\frac{1}{6!}\right]$
$=360-120+30-6+1$
$=391-126=265$