document.write( "Question 1081093: Four letters and envelops are addressed to four different people.if the lettersare randomly inserted into the enevlopes,what is the probabilitythat
\n" ); document.write( "a)exactly one will be insertedin the correct enevolop,and b)at $east one willbe insertedin the corr3ct en3vlop? \n" ); document.write( "

Algebra.Com's Answer #695215 by Edwin McCravy(20067) $\"\"$ $\"About$

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Four letters and envelopes are addressed to four different people. If the letters are randomly inserted into the envelopes,what is the probability
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\n" ); document.write( "one will be inserted in the correct envelope?\r
\n" ); document.write( "\n" ); document.write( "There are 4! ways the letters can be sent.\r
\n" ); document.write( "\n" ); document.write( "We first find the probability of the complement event, that all of the
\n" ); document.write( "letters are in the wrong envelope:\r
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\n" ); document.write( "\n" ); document.write( "First we find the number of ways they can all be in wrong envelopes\r
\n" ); document.write( "\n" ); document.write( "Envelope 1 2 3 4
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\n" ); document.write( "Letters 2 1 4 3
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document.write( "Letters     2   3   4   1
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document.write( "Letters     2   4   1   3
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document.write( "Letters     3   1   4   2
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document.write( "Letters     3   4   1   2
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document.write( "Letters     3   4   2   1
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document.write( "Letters     4   1   2   3
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document.write( "Letters     4   3   1   2
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document.write( "Letters     4   3   2   1\r
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document.write( "Count them.  That's 9 ways they can all go wrong.\r
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document.write( "So the probability that they are all wrong is 9 ways out of 24,
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document.write( "or 9/24.\r
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document.write( "So the correct probability is 1 - 9/24 = 24/24 - 9/24 = 15/24 = 5/8
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