Algebra.Com's Answer #846056 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "A family of 6 boys and 4 girls. Mother wanted to choose 4 of them to prepare dinner:
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document.write( "What is the probability of choosing a boy to prepare tea, a boy to cook, and two girls to process
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document.write( "The total number of ways to assign jobs  is\r\n" );
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document.write( "  = 10*9*28 = 2520.\r\n" );
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document.write( "(10 ways to fill the first position; 9 ways to fill the second position;\r\n" );
document.write( "and  = 28 ways to fill the 3-rd and 4-th positions with possible transposition there).\r\n" );
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document.write( " | Now let's calculate the number of ways |\r\n" );
document.write( " | to assign jobs as described. |\r\n" );
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document.write( "The number of ways to select one boy from 6 boys to prepare tea is 6. \r\n" );
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document.write( "The number of ways to select 1 boy from remaining 5 boys to cook is 5.\r\n" );
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document.write( "The number of ways to select 2 girls from 4 girls is  =  = 6.\r\n" );
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document.write( "So, the number of ways to form a proper team as described is 6*5*6 = 180.\r\n" );
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document.write( "The probability under the problem's question is\r\n" );
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document.write( " number of proper ways 180 1\r\n" );
document.write( " P = ------------------------- = ----- = ---- = 0.07143 (rounded). ANSWER\r\n" );
document.write( " total number of ways 2520 14\r\n" );
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document.write( " | Another way to solve is to write |\r\n" );
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document.write( " P =  =  =  (the same answer).\r\n" );
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document.write( "Here  is the probability to select one of 6 boys from 10 kids to prepare tea.\r\n" );
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document.write( "  is the probability to select one of remaining 5 boys from remaining 9 kids to cook.\r\n" );
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document.write( "  =  is the probability to select one of 6 possible pairs (girl,girl) \r\n" );
document.write( " from 28 possible pairs (kid,kid) to process table.\r\n" );
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document.write( "Solved in two ways, for your better understanding.\r
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document.write( "A TWIN problem was solved at this forum several days ago under this link\r
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document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1207851.html\r
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