Question

A person writes 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

Options

•  \[\frac{1}{4}\]

• \[\frac{11}{24}\]

• \[\frac{15}{24}\]

   

• \[\frac{23}{24}\]

Answer 1

\[ \frac{23}{24}\]

4 letters can be placed in 4 envelopes in 4! ways = 24 ways
Now, there is only one method, by which all the letters are placed in the right envelope.

P(all letters are placed in the right envelopes) = \[\frac{1}{24}\] P(all letters are not placed in the right envelopes) = 1 - P(all letters are placed in the right envelopes)

\[= 1 - \frac{1}{24}\]
\[ = \frac{23}{24}\]