You can
put this solution on YOUR website! A typist has 5 letters and 5 addressed envelope. in how many
different ways can the letters be placed in each envelope without
getting every letter in the right envelope?
There are 5!=120 ways they can be placed. Only 1 of those 120 ways
has every letter in the right envelope. So there are 119 ways that
not every letter gets in the right envelope.
Answer: 119 out of 120 = 119/120
If the letter are placed in the envelopes at random, what is the
probability that each letter is in its correct envelope?
Answer: 1 way out of 120 or 1/120
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You weren't asked for the probability that all 5 letters are in
the wrong envelope. That involves the concept of derangements
which involves the "sub-factorial" function.
Here's the answer to that: 44 ways out of 120 = 44/120 = 11/30
Edwin
