Question

There are $4$ envelopes corresponding to $4$ letters. If the letters are placed in the envelopes at random, what is the probability that all the letters are not placed in the right envelopes?

• A. $20/24$
• B. $1/24$
• C. $23/24$
• D. $4/24$

Answer 1

The correct option is C $23/24$

Ways of keeping 4 letters in 4 envelopes $=4!=24$
For the letters to be put in their correct envelopes,there is only 1 way.
Hence,probability that all letters are not put in correct envelopes$=$1$-$(probability that letters are put in correct envelopes)$=1-\frac{1}{24}=\frac{23}{24}$