SOLUTION: Four letters and envelops are addressed to four different people.if the lettersare randomly inserted into the enevlopes,what is the probabilitythat a)exactly one will be inserted

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Question 1081093: Four letters and envelops are addressed to four different people.if the lettersare randomly inserted into the enevlopes,what is the probabilitythat
a)exactly one will be insertedin the correct enevolop,and b)at $east one willbe insertedin the corr3ct en3vlop?
Answer by Edwin McCravy(20067) About Me  (Show Source):
You can put this solution on YOUR website!
Four letters and envelopes are addressed to four different people. If the letters are randomly inserted into the envelopes,what is the probability
that
a)exactly one will be inserted in the correct enevelope, and b)at least
one will be inserted in the correct envelope?
There are 4! ways the letters can be sent.
We first find the probability of the complement event, that all of the
letters are in the wrong envelope:

First we find the number of ways they can all be in wrong envelopes
Envelope 1 2 3 4
-------------------------
Letters 2 1 4 3


Letters     2   3   4   1

Letters     2   4   1   3

Letters     3   1   4   2

Letters     3   4   1   2

Letters     3   4   2   1

Letters     4   1   2   3

Letters     4   3   1   2

Letters     4   3   2   1



Count them.  That's 9 ways they can all go wrong.



So the probability that they are all wrong is 9 ways out of 24,

or 9/24.



So the correct probability is 1 - 9/24 = 24/24 - 9/24 = 15/24 = 5/8