A clerk has 4 different letters that need to go in 4 different envelopes. What is the probability that all 4 letters are placed in the correct envelopes?

1 Answer
Shwetank Mauria
Jun 13, 2017

The probability that all #4# letters are placed in the correct envelopes is #1/24#.

Explanation:

Let us first question how many ways are there in which we can place #4# letters in #4# different envelopes.

The answer is #color(white) - ^4P_4=4xx3xx2xx=24#.

But there is only one way of pacing letters in correct envelopes, of course assuming that addressees areall different.There are

Hence, the probability that all #4# letters are placed in the correct envelopes is #1/24#.

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