A man writes 5 letters, one each to A, B, C, D and E. Each letter is placed in a separate envelope and sealed. He then addressed the envelopes, at random, one each to A, B, C, D and E.
Find the probability that both of the letters to A and B are in incorrect envelopes.
The answer is given as 13/20 but I can't figure out why. Can anyone help?
Hello, jjc!
Here is a logical (but very primitive) approach . . .A man writes 5 letters, one each to A, B, C, D and E.
Each letter is placed in a separate envelope and sealed.
He then addressed the envelopes, at random, one each to A, B, C, D and E.
Find the probability that both of the letters to A and B are in incorrect envelopes.
Answer:
The letters are: .
Their envelopes are: .
There are two cases to consider:
. . (1) Letter is in envelope
. . (2) Letter is not in envelope
(1) Letter is in envelope : .
Then letter can go in any of the other four envelopes:
. .
Hence: .
(2) Letter is in not in envelope ... it is in
. .
Then letter B must be in one of the three remaining envelopes.
. .
Hence: .
Therefore: .