document.write( "Question 927667: a) In how many ways can a committee consisting of three men and two women be chosen from seven men and five women?
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\n" ); document.write( "d) Find the number of permutations that can be formed from the letters UNUSUAL?
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Algebra.Com's Answer #563175 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
a) In how many ways can a committee consisting of three men and two women be chosen from seven men and five women?
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document.write( "We can choose the 3 men C(7,3) ways. \r\n" );
document.write( "For each of those ways, we can choose the 2 women C(5,2) ways.\r\n" );
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document.write( "Answer C(7,3)C(5,2) = 35*10 = 350 ways\r\n" );
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\n" ); document.write( "b) How many committee of five with a given chairman can be selected from twelve persons?
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document.write( "I can't tell for sure whether you mean that we must select only one particular\r\n" );
document.write( "man, say John Smith, as the only person who can be the chairman, and none of the\r\n" );
document.write( "other 11 can be the chairman. \r\n" );
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document.write( "or whether \r\n" );
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document.write( "Any of the 12 men can be the chairman.\r\n" );
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document.write( "So I'll do it both ways:\r\n" );
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document.write( "A.  If it's the first way (which I doubt), then \r\n" );
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document.write( "we choose theit chairman 1 way, C(1,1), as John Smith,\r\n" );
document.write( "then we choose the 4 non-chairmen C(11,4) ways.\r\n" );
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document.write( "Answer: if it's that way:  C(1,1)*C(11,4) = 1*330 = 330 ways.\r\n" );
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document.write( "B.  If it's the second way (which I suspect),   \r\n" );
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document.write( "There are two correct ways to approach the problem:  Choose the chairman first,\r\n" );
document.write( "and then choose the 4 non-chairmen, OR choose the committee first, then choose\r\n" );
document.write( "the chairman.\r\n" );
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document.write( "   1.  We can pick the chairman 12 ways.  C(12,1)\r\n" );
document.write( "       For each of those ways we can then choose the 4 non-chairmen C(11,4)\r\n" );
document.write( "       ways.\r\n" );
document.write( "       Answer: C(12,1)C(11,4) = 12*330 = 3960 ways.  \r\n" );
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document.write( "   2.  We can pick the committee C(12,5) ways.\r\n" );
document.write( "       For each way to pick a committee we can pick a chairman 5 ways. C5,1)\r\n" );
document.write( "       Answer: C(12,5)C(5,1) = 792*5 = 3960 ways.\r\n" );
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document.write( "Take your pick of those two.  They are both correct. Notice that although they\r\n" );
document.write( "multiply different numbers they both end up giving the same answer 3960.\r\n" );
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\n" ); document.write( "c) In how many ways can a teacher choose one or more students from six eligible students?
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document.write( "Let the 6 students be A,B,C,D,E, and F.\r\n" );
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document.write( "The teacher can make 2 choices about A.  They are: \r\n" );
document.write( "1. Choose A  \r\n" );
document.write( "2. Don't choose A\r\n" );
document.write( "That's 2 choices the teacher can make about A.\r\n" );
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document.write( "For each of those 2 choices the teacher can make about A,\r\n" );
document.write( "the teacher can make 2 choices about B.  They are: \r\n" );
document.write( "1. Choose B  \r\n" );
document.write( "2. Don't choose B.\r\n" );
document.write( "That's 2*2=22 = 4 choices the teacher can make about A and B.\r\n" );
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document.write( "For each of those 4 choices the teacher can make about A and B,\r\n" );
document.write( "the teacher can make 2 choices about C.  They are: \r\n" );
document.write( "1. Choose C  \r\n" );
document.write( "2. Don't choose C.\r\n" );
document.write( "That's 2*2*2=23 = 8 choices the teacher can make about A,B and C.\r\n" );
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document.write( "For each of those 8 choices the teacher can make about A,B and C,\r\n" );
document.write( "the teacher can make 2 choices about D.  They are: \r\n" );
document.write( "1. Choose D  \r\n" );
document.write( "2. Don't choose D.\r\n" );
document.write( "That's 2*2*2*2=24 = 16 choices the teacher can make about A,B,C, and D.\r\n" );
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document.write( "For each of those 16 choices the teacher can make about A,B,C and D,\r\n" );
document.write( "the teacher can make 2 choices about E.  They are: \r\n" );
document.write( "1. Choose E  \r\n" );
document.write( "2. Don't choose E.\r\n" );
document.write( "That's 2*2*2*2*2=25 = 32 choices the teacher can make about A,B,C,D, and E.\r\n" );
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document.write( "For each of those 32 choices the teacher can make about A,B,C,D, and E,\r\n" );
document.write( "the teacher can make 2 choices about F.  They are: \r\n" );
document.write( "1. Choose F  \r\n" );
document.write( "2. Don't choose F.\r\n" );
document.write( "That's 2*2*2*2*2*2=26 = 64 choices the teacher can make about A,B,C,D,E and F.\r\n" );
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document.write( "However, among those 64 possible choices the teacher can make, we must\r\n" );
document.write( "eliminate the one case where the teacher does not choose any of the 6 \r\n" );
document.write( "students.  So we must subtract that 1 case from the 64.\r\n" );
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document.write( "Answer: 64-1 = 63 \r\n" );
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\n" ); document.write( "d) Find the number of permutations that can be formed from the letters UNUSUAL?
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document.write( "If the 3 U's looked different (were distinguishable like this\r\n" );
document.write( "UNUSUAL, the answer would be 7! \r\n" );
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document.write( "However, since we cannot tell the difference between the U's, we\r\n" );
document.write( "must divide by the number of positions the three U's can be placed\r\n" );
document.write( "within each permutation, which is 3! so the answer is \"7%21%2F3%21=5040%2F6=840\" ways.\r\n" );
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document.write( "Edwin
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