Question

A person write 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is
(a) 1/4
(b) 11/24
(c) 15/24
(d) 23/24

Answer 1

(d) $\frac{23}{24}$

Total number of ways of placing four letters in 4 envelops = 4! = 24
All the letters can be dispatched in the right envelops in only one way. Therefore, the probability that all the letters are placed in the right envelops is $\frac{1}{24}$.
Hence, probability that all the letters are not placed in the right envelops = $1-\frac{1}{24}=\frac{23}{24}$