document.write( "Question 1203282: 4 boys and 5 girls are asked to form a line. In how many ways can this be done?
\n" ); document.write( "Find also the number of arrangements in which
\n" ); document.write( "a) The first two are girls
\n" ); document.write( "b) The first is a boy and the last is a girl
\n" ); document.write( "c) The boys are together
\n" ); document.write( "d) No two girls stand next to each other \n" ); document.write( "

Algebra.Com's Answer #838732 by ikleyn(52879) $\"\"$ $\"About$

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\n" ); document.write( "4 boys and 5 girls are asked to form a line. In how many ways can this be done?
\n" ); document.write( "Find also the number of arrangements in which
\n" ); document.write( "a) The first two are girls
\n" ); document.write( "b) The first is a boy and the last is a girl
\n" ); document.write( "c) The boys are together
\n" ); document.write( "d) No two girls stand next to each other
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document.write( "(_)  For the question, not marked by a letter, the answer is (4+5)! = 9! = 1*2*3*4*5*6*7*8*9 = 362,880.\r\n" );
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document.write( "a)  (5*4) = 20 different choices for the first two girls, \r\n" );
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document.write( "    and (9-2)! = 7! = 1*2*3*4*5*6*7 = 5040 permutations for the rest (9-2) = 7 persons.\r\n" );
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document.write( "    Total is  (5*4)*7! = 20*5040 = 100,800 different ways.\r\n" );
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document.write( "(b)  4 different choices for the first boy;\r\n" );
document.write( "     5 different choices for the last girl;\r\n" );
document.write( "     and 7! different permutations for the rest of participants.\r\n" );
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document.write( "     The total is (4*5)*7! = 20*7! = 100,800 different ways.\r\n" );
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document.write( "(c)  6 choices to place the block of 4 boys in the line;\r\n" );
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document.write( "     4! = 24 permutations of 4 boys inside this block\r\n" );
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document.write( "     and 5! = 120 permutations for the 5 (five) girls.\r\n" );
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document.write( "     In all, it gives  6*24*120 = 17280 different ways.\r\n" );
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document.write( "(d)  The scheme is unique: the girls are in positions numbered by odd digits from 1 to 9;\r\n" );
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document.write( "                           the boys  are in positions numbered by even digits from 1 to 9.\r\n" );
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document.write( "     Inside this scheme, 5! = 120 permutations are available for girls and 4! = 24 permutations for boys.\r\n" );
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document.write( "     In all,  120*24 = 2880 different ways.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
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\n" ); document.write( "\n" ); document.write( "Do not forget to post your \"THANKS\" to me for my teaching.\r
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