document.write( "Question 1208918: A history class is comprised of 5
\n" ); document.write( "female and
\n" ); document.write( "9 male students. If the instructor of the class randomly chooses
\n" ); document.write( "8 students from the class for an oral exam, what is the probability that
\n" ); document.write( "3 female students and
\n" ); document.write( "5 male students will be selected? Round your answer to
\n" ); document.write( "decimal places \n" ); document.write( "

Algebra.Com's Answer #847453 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A history class is comprised of 5 female and 9 male students.
\n" ); document.write( "If the instructor of the class randomly chooses 8 students from the class for an oral exam,
\n" ); document.write( "what is the probability that 3 female students and 5 male students will be selected?
\n" ); document.write( "Round your answer to decimal places.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The correct formula for the probability is \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    P = \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Here the denominator is the number of all possible different unordered sets of 8 students\r\n" );
document.write( "to be selected from 5+9 = 14 students.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In the numerator, C[5]^3 represents the number of all possible different triplets of female\r\n" );
document.write( "students selected from 5 female students;\r\n" );
document.write( "\r\n" );
document.write( "                  C[9]^5 represents the number of all possible different quintuplets of male\r\n" );
document.write( "students selected from 9 male students.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now,   =  = 10;\r\n" );
document.write( "\r\n" );
document.write( "       =  = 126;\r\n" );
document.write( "\r\n" );
document.write( "       =  = 3003.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, the  ANSWER  is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    P =  = 0.41958042\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and you can round it in any way you need.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The calculations of the binomial coefficients can be done manually or using technology.\r
\n" ); document.write( "\n" ); document.write( "I personally use MS Excel in my computer, by copying-pasting the formula into it,
\n" ); document.write( "or the standard Excel function COMBIN.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Here in my solution, I used the notion/(the conception) of COMBINATIONS.
\n" ); document.write( "Actually, when you get such a problem, it is assumed in the regular/normal course of education
\n" ); document.write( "that you are familiar with this conception and relevant formulas.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you are not familiar with it, in clear and compact form it is given in the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Introduction to Combinations\r
\n" ); document.write( "\n" ); document.write( "    - PROOF of the formula on the number of Combinations\r
\n" ); document.write( "\n" ); document.write( "    - Problems on Combinations\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );