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. \(\frac{1}{4}\)

B. \(\frac{11}{24}\)

C. \(\frac{15}{24}\)

D. \(\frac{3}{8}\)

Answer 1

As we have 4 letters and 4 envelopes. 

These 4 letters can be arranged in 4! = 24 ways. 

∴ n(S) = 24 

Let E denotes the event that all letters are not placed in the right envelopes 

The number of ways in which 4 letters can be placed in wrong envelopes is given by the number of ways in which N objects can be de-arranged. 

Numbers of ways of in which N objects can be de-arranged is given by –

∴ P(E) = \(\frac{9}{24}\)  = \(\frac{ 3}{8}\)