document.write( "Question 1207851: A family of 6 boys and 3 girls. Mother wanted to choose 4 of them to prepare dinner:
\n" ); document.write( "What is the probability of choosing a boy to prepare tea, a boy to cook, and two girls to process
\n" ); document.write( "Table?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #845980 by ikleyn(52855) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A family of 6 boys and 3 girls. Mother wanted to choose 4 of them to prepare dinner:
\n" ); document.write( "What is the probability of choosing a boy to prepare tea, a boy to cook, and two girls
\n" ); document.write( "to process Table?
\n" ); document.write( "~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The total number of ways to assign jobs    is\r\n" );
document.write( "\r\n" );
document.write( "     = 9*8*21 = 1512.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(9 ways to fill the first position; 8 ways to fill the second position;\r\n" );
document.write( "and  ways to fill the 3-rd and 4-th positions with possible transposition there).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    +-------------------------------------------+\r\n" );
document.write( "    |   Now let's calculate the number of ways  |\r\n" );
document.write( "    |      to assign jobs as described.         |\r\n" );
document.write( "    +-------------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The number of ways to select one boy from 6 boys to prepare tea is 6.            \r\n" );
document.write( "\r\n" );
document.write( "The number of ways to select 1 boy from remaining 5 boys to cook is 5.\r\n" );
document.write( "\r\n" );
document.write( "The number of ways to select 2 girls from 3 girls is 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the number of ways to form a proper team as described is 6*5*3 = 90.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The probability under the problem's question is\r\n" );
document.write( "\r\n" );
document.write( "          number of proper ways       90     5\r\n" );
document.write( "    P = ------------------------- = ----- = ---- = 0.05952  (rounded).    ANSWER\r\n" );
document.write( "          total number of ways       1512    84\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    +---------------------------------------+\r\n" );
document.write( "    |   Another way  to solve is to write   |\r\n" );
document.write( "    +---------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    P =  =  =   (the same answer).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Here    is the probability to select one of 6 boys from 9 kids to prepare tea.\r\n" );
document.write( "\r\n" );
document.write( "        is the probability to select one of remaining 5 boys from remaining 8 kids to cook.\r\n" );
document.write( "\r\n" );
document.write( "        is the probability to select two of 3 girls from remaining 7 kids to process table.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved in two ways, for your better understanding.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );