document.write( "Question 952834: 16 people ( 10 men & 6 women) are on a team. How many different ways can the team chose a captain, manager, assistant coach if:
\n" ); document.write( " a. the manager must be a woman\r
\n" ); document.write( "\n" ); document.write( " b. the captain must be robert (one of the men)\r
\n" ); document.write( "\n" ); document.write( " c. at least one man and one women must be chosen for the 3 distinct positions \n" ); document.write( "

Algebra.Com's Answer #581995 by Edwin McCravy(20056) $\"\"$ $\"About$

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16 people ( 10 men & 6 women) are on a team. How many different
\n" ); document.write( "ways can the team chose a captain, manager, assistant coach if:
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document.write( "Rule:  Always choose the most restrictive situations first.\r\n" );
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\n" ); document.write( "a. the manager must be a woman
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document.write( "Choose the woman for the manager any of 6 ways.\r\n" );
document.write( "That leaves 15 ways to choose the captain.\r\n" );
document.write( "That leaves 14 ways to choose the assistant coach.\r\n" );
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document.write( "Answer: 6*15*14 = 1260 ways.\r\n" );
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\n" ); document.write( "b. the captain must be robert (one of the men)
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document.write( "Choose Robert for the captain 1 way.\r\n" );
document.write( "That leaves 15 ways to choose the manager\r\n" );
document.write( "That leaves 14 ways to choose the assistant coach.\r\n" );
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document.write( "Answer: 1*15*14 = 210 ways.\r\n" );
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\n" ); document.write( "c. at least one man and one women must be chosen for
\n" ); document.write( "the 3 distinct positions
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document.write( "We use the indirect method.\r\n" );
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document.write( "All choices - undesirable choices = desirable choices.\r\n" );
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document.write( "All choices:\r\n" );
document.write( "Choose the captain any of 16 ways.\r\n" );
document.write( "That leaves 15 ways to choose the manager\r\n" );
document.write( "That leaves 14 ways to choose the assistant coach.\r\n" );
document.write( "That's 16*15*14 = 3360 ways.\r\n" );
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document.write( "Undesirable choices of all three men:\r\n" );
document.write( "Choose the captain any of 10 ways.\r\n" );
document.write( "That leaves 9 ways to choose the manager\r\n" );
document.write( "That leaves 8 ways to choose the assistant coach.\r\n" );
document.write( "That's 10*9*8 = 720 ways to choose all men.\r\n" );
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document.write( "Undesirable choices of all three women:\r\n" );
document.write( "Choose the captain any of 6 ways.\r\n" );
document.write( "That leaves 5 ways to choose the manager\r\n" );
document.write( "That leaves 4 ways to choose the assistant coach.\r\n" );
document.write( "That's 6*5*4 = 120 ways to choose all women.\r\n" );
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document.write( "Answer: 3360 - 720 - 120 = 2520 desirable ways.\r\n" );
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document.write( "Edwin

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