document.write( "Question 1194074: Four girls and three boys are seated randomly in a row. Calculate the following probabilities.
\n" ); document.write( "(a) The girls occupy the first three places.
\n" ); document.write( "(b) They are arranged to alternate girl, boy, girl, etc. \r
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\n" ); document.write( "(a) 4/35
\n" ); document.write( "(b) 1/35\r
\n" ); document.write( "\n" ); document.write( "Can someone explain the answers? Thank you.\r
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Algebra.Com's Answer #826171 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
Four girls and three boys are seated randomly in a row. Calculate the following probabilities.
\n" ); document.write( "(a) The girls occupy the first three places.
\n" ); document.write( "(b) They are arranged to alternate girl, boy, girl, etc.
\n" ); document.write( "Answers
\n" ); document.write( "(a) 4/35
\n" ); document.write( "(b) 1/35
\n" ); document.write( "Can someone explain the answers? Thank you.
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document.write( "(a)  The total number of all possible different permutations/arrangements, without any constraints, is\r\n" );
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document.write( "         (4+3)! = 7! = 1*2*3*4*5*6*7.\r\n" );
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document.write( "     If the girls occupy first three position, then the number of all such permutations/arrangements is\r\n" );
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document.write( "         (4*3*2) * (7-3)! = (4*3*2) * (4*3*2*1).\r\n" );
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document.write( "     The probability under question (a) is the ratio of these numbers\r\n" );
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document.write( "         P = {{({(4*3*2)*(4*3*2*1))/(1*2*3*4*5*6*7)}}} = .    ANSWER\r\n" );
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document.write( "(b)  There is only one placing scheme, satisfying conditions (b). It is  (G B G B G B G).\r\n" );
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document.write( "     Inside this scheme, 4! * 3! arrangements are possible.\r\n" );
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document.write( "     In all, there are 7! arrangements of 4 girls and 3 boys.\r\n" );
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document.write( "     The ratio of these two numbers is the sough probability  P = .\r\n" );
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document.write( "     Reduce this fraction and get the answer  .\r\n" );
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