document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202251>Question 1202251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of committees consisting of 4 men and 5 women that can be formed from 10 men and 13 women is  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836940 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=836940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "None of the seats on the committee have a label (eg: \"president\" or \"treasurer\"), which means order does not matter. <BR>\n" );
document.write( "No member outranks another.<BR>\n" );
document.write( "A group like {A,B,C} is the same as {B,C,A}.\r<BR>\n" );
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document.write( "Since order doesn't matter, we use the nCr combination formula.\r<BR>\n" );
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document.write( "Let's find out how many ways there are to select the men.<BR>\n" );
document.write( "n = 10 men total<BR>\n" );
document.write( "r = 4 men to select<BR>\n" );
document.write( "n C r = (n!)/(r!(n-r)!)<BR>\n" );
document.write( "10 C 4 = (10!)/(4!*(10-4)!)<BR>\n" );
document.write( "10 C 4 = (10!)/(4!*6!)<BR>\n" );
document.write( "10 C 4 = (10*9*8*7*6!)/(4!*6!)<BR>\n" );
document.write( "10 C 4 = (10*9*8*7)/(4!)<BR>\n" );
document.write( "10 C 4 = (10*9*8*7)/(4*3*2*1)<BR>\n" );
document.write( "10 C 4 = 5040/24<BR>\n" );
document.write( "10 C 4 = 210<BR>\n" );
document.write( "There are 210 ways to select the four men from a candidate pool of ten men. Order doesn't matter.\r<BR>\n" );
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document.write( "nCr calculator<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php\">https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php</a><BR>\n" );
document.write( "This is one of many free online calculators that specialize in computing the nCr combination value.\r<BR>\n" );
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document.write( "If you have a TI84 or similar, then check out this example video. <BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.youtube.com/watch?v=wxlJcZzJgpo\">https://www.youtube.com/watch?v=wxlJcZzJgpo</a><BR>\n" );
document.write( "Coincidentally, the person goes over 10C4 = 210\r<BR>\n" );
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document.write( "The value 210 can be found in Pascal's Triangle. <BR>\n" );
document.write( "Look at the row that starts with 1,10,...<BR>\n" );
document.write( "Count 5 spaces to arrive at 210. <BR>\n" );
document.write( "We count 5 spaces, and not 4, because the index starts at r = 0.\r<BR>\n" );
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document.write( "Use whichever method you prefer (calculator, formula, pascals triangle) to find that 13C5 = 1287 is the number of ways to pick the five women from a candidate pool of thirteen women.\r<BR>\n" );
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document.write( "Overall we have:<BR>\n" );
document.write( "(10C4)*(13C5) = 210*1287 = 270270<BR>\n" );
document.write( "ways to form this committee.\r<BR>\n" );
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document.write( "Answer: <font color=\"red\" size=4>270270</font><BR>\n" );
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