SOLUTION: 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? If the le

Question 1043764: 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? If the letter are placed in the envelopes at random, what is the probability that each letter is in its correct envelope?
Answer by Edwin McCravy(20055) (Show Source): 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

----------

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

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