document.write( "Question 848963: An apartment block has 8 tenants, each with
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\n" ); document.write( "(a) (4 points) How many ways can the
\n" ); document.write( "mail be delivered if three tenants get
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\n" ); document.write( "(b) (5 points) In how many ways can the
\n" ); document.write( "mail be delivered if the only restriction
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Algebra.Com's Answer #512072 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
An apartment block has 8 tenants, each with
\n" ); document.write( "a separate mail slot. Eleven different pieces
\n" ); document.write( "of junk mail are delivered.
\n" ); document.write( "(a) (4 points) How many ways can the
\n" ); document.write( "mail be delivered if three tenants get
\n" ); document.write( "two pieces of junk mail and five get one
\n" ); document.write( "piece?
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document.write( "Suppose the mail slots are numbered 1,2,3,4,5,6,7,8\r\n" );
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document.write( "Pick the 3 mail slots to get 2 pieces in C(8,3) ways.\r\n" );
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document.write( "Pick the 2 pieces of junk mail to put in the lowest numbered \r\n" );
document.write( "mail slot that gets 2 pieces in C(11,2) ways. \r\n" );
document.write( "Pick the 2 pieces of junk mail to put in the next lowest numbered \r\n" );
document.write( "mail slot that gets 2 pieces in C(9,2) ways. \r\n" );
document.write( "Pick the 2 pieces of junk mail to put in the highest numbered \r\n" );
document.write( "mail slot that gets 2 pieces in C(7,2) ways. \r\n" );
document.write( "The remaining 5 pieces of mail can be delivered to the remaining\r\n" );
document.write( "5 boxes in P(5,5) or 5! or 120 ways.\r\n" );
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document.write( "Answer: C(8,3)×C(11,2)×C(9,2)×C(7,2)×5! = 56×55×36×21×120 = 279417600\r\n" );
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\n" ); document.write( "(b) (5 points) In how many ways can the
\n" ); document.write( "mail be delivered if the only restriction
\n" ); document.write( "is that every tenant gets at least one
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document.write( "We can distribute the 11 pieces of junk mail these ways\r\n" );
document.write( "1. 4 in one box, 1 each in the other 7 boxes\r\n" );
document.write( "   pick the box to get four in 8 ways. \r\n" );
document.write( "   Pick the pieces of junk mail to go in it C(11,4) ways.\r\n" );
document.write( "   Pick the way to place the 7 remaining pieces of junk mail 7! ways.\r\n" );
document.write( "   That's 8×C(11,4)×7! = 8×330×5040 = 13305600\r\n" );
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document.write( "2. 3 in one box, 2 in one box and 1 each in the other 6 boxes \r\n" );
document.write( "   pick the box to get 3 in 8 ways.\r\n" );
document.write( "   pick the box to get 2 in 7 ways.\r\n" );
document.write( "   pick the pieces of junk mail to go in the box that is to get 3 in\r\n" );
document.write( "   C(11,3) ways.\r\n" );
document.write( "   pick the pieces of junk mail to go in the box that is to get 2 in \r\n" );
document.write( "   C(8,2) ways.\r\n" );
document.write( "   Pick the way to place the 6 remaining pieces of junk mail 6! ways.\r\n" );
document.write( "   That's 8×7×C(11,3)×C(8,2)×6! = 8×7×165×28×720 = 186278400\r\n" );
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document.write( "3. 2 in one box, 2 in another box and 2 in a third box and 1 each in the \r\n" );
document.write( "   other 5 boxes \r\n" );
document.write( "   pick the three boxes to get 2 in C(8,3) ways. \r\n" );
document.write( "   pick the 2 pieces of mail to go in the lowest numbered box of those \r\n" );
document.write( "   three that get two in C(11,2) ways\r\n" );
document.write( "   pick the 2 pieces of mail to go in the next higher numbered box of those\r\n" );
document.write( "   three that get two in C(9,2) ways\r\n" );
document.write( "   pick the 2 pieces of mail to go in the highest numbered box of those\r\n" );
document.write( "   three that get two in C(7,2) ways   \r\n" );
document.write( "   Pick the way to place the 5 remaining pieces of junk mail 5! ways.\r\n" );
document.write( "   That's C(8,3)×C(11,2)×C(9,2)×C(7,2)×5! = 56×55×36×21×120 = 249417600\r\n" );
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document.write( "Answer:  Total = 13305600+186278400+249417600 = 479001600\r\n" );
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document.write( "Edwin
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