Q. 194.0( 4 Votes )

# 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. 3/8

Answer :

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 dearranged.

Numbers of ways of in which N objects can be dearranged is given by –

∴ n(E) =

∴ P(E) = 9/24 = 3/8

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