document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1048812>Question 1048812</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP!! I REALLY NEED HELP!\r<BR>\n" );
document.write( "\n" );
document.write( "A jury pool consists of 30 people, 16 men and 14 women. Compute the probability that a randomly selected jury of 12 people is all male. (Give your answer as a fraction.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #664379 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=664379\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> number of ways you can get 12 men out of 16 men is c(16,12) = 1820.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "number of ways you can get 14 jurors out of 30 people is c(30,12) = 145422675.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability that the jury will consist of all men is 1820 / 86493225 = 2.104211052 * 10^-5 which is equal to .00002104211052.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "look at it another way.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability that you can draw 1 man out of 30 jurors when 16 of them are men would be 16/30.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability that you will draw 12 men in a row would then be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "16/30 * 15/29 * 14/28 * 13/27 * 12/26 * 11/25 * 10/24 * 9/23 * 8/22 * 7/21 * 6/20 * 5/19\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's equal to  .00002104211052\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "same answer either way, so the solution looks good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the calculator might show the answer as 2.104211052 * 10^(-5).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the same as 2.104211052 / 100,000 which is equal to .00002104211052.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability of any occurrence is the number of ways it can occur divided by the total number of ways all possible combinations can occur.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that would be the number of possible ways 12 men can occur divided by the number of ways 12 jurors can occur whether or not they are men or women.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c(16,12) is the number of ways you can get 12 men out of 16 possible men.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c(30,12) is the number of ways you can get 12 jurors out of 30 possible juror whether or not they are men or women.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the combination formula is c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when you have 16 possible men and need to select 12 out of them, the formula becomes c(16,12) which is equal to 16! / (12! * 4!) which is equal to 1820\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when you have 30 possible jurors and need to select 12 out of them, the formula becomes c(30,12) = 30! / (18! * 12!) which is equal to 86493225.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1820 / 86493225= 2.104211052 * 10^(-5) which is equal to .00002104211052.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );