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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
Options
1/4
11/24
15/24
23/24
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Solution
\[\frac{23}{24}\] Total number of ways of placing four letters in 4 envelops = 4! = 24
All the letters can be dispatched in the right envelops in only one way. Therefore, the probability that all the letters are placed in the right envelops is \[\frac{1}{24}\] .
Hence, probability that all the letters are not placed in the right envelops = \[1 - \frac{1}{24} = \frac{23}{24}\]
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