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Question
A person writes a letter to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wrong places?
A person writes a letter to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wrong places?
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Solution
The correct option is A 719
The number of possible way of putting 6 letters into 6 envelopes = 6!
Number of ways to place all letters correctly into corresponding envelopes =1
Number of ways to place one letter in the wrong envelope and other 5 letters in the write envelopes =0
It is not possible that only one letter goes in the wrong envelope when 5 letters goes in the right envelope, then remaining letter one letter also goes in wright envelope.
Number of ways to place at least two letters goes in the wrong envelopes = 6! - 0 - 1 = 720 -1 = 719
719
The number of possible way of putting 6 letters into 6 envelopes = 6!
Number of ways to place all letters correctly into corresponding envelopes =1
Number of ways to place one letter in the wrong envelope and other 5 letters in the write envelopes =0
It is not possible that only one letter goes in the wrong envelope when 5 letters goes in the right envelope, then remaining letter one letter also goes in wright envelope.
Number of ways to place at least two letters goes in the wrong envelopes = 6! - 0 - 1 = 720 -1 = 719
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