document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=758282>Question 758282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are n men and 4 women from which a 3 person committee is to be formed. What is the probability of selecting 1 or 2 women in the group?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #461367 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=461367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the probability is:\r<BR>\n" );
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document.write( "(nC2 * 4C1) / ((n+4)C3)\r<BR>\n" );
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document.write( "plus:\r<BR>\n" );
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document.write( "(nC1 * 4C2) / ((n+4)C3)\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "let n = 2\r<BR>\n" );
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document.write( "this means you have 2 men to choose from and 4 women to choose from which give you a total of 6 persons to choose from (2 + 4 = 6).\r<BR>\n" );
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document.write( "the number of possible combinations of getting 3 people out of 6 is equal to 6C3 which is equal to 20.\r<BR>\n" );
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document.write( "the number of ways of getting 2 men and 1 women would be equal to 2C2 * 4C1 which is equal to 1 * 4 which is equal to 4.\r<BR>\n" );
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document.write( "the number of ways of getting 1 man and 2 women would be equal to 2C1 * 4C2 which is equal to 2 * 6 which is equal to 12.\r<BR>\n" );
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document.write( "the number of ways of getting 3 women would be equal to 4C3 which is equal to 4.\r<BR>\n" );
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document.write( "if you let a,b represent the men and you let c,d,e,f represent the women, then the possible combinations are:\r<BR>\n" );
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document.write( "total of 4 ways to get 2 men and 1 woman as shown below:\r<BR>\n" );
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document.write( "a,b,c<BR>\n" );
document.write( "a,b,d<BR>\n" );
document.write( "a,b,e<BR>\n" );
document.write( "a,b,f\r<BR>\n" );
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document.write( "total of 6 ways to get 1 man and 2 women where the man is represented by a.\r<BR>\n" );
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document.write( "a,c,d<BR>\n" );
document.write( "a,c,e<BR>\n" );
document.write( "a,c,f<BR>\n" );
document.write( "a,d,e<BR>\n" );
document.write( "a,d,f<BR>\n" );
document.write( "a,e,f\r<BR>\n" );
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document.write( "total of 6 ways to get 1 man and 2 women where the man is represented by b.\r<BR>\n" );
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document.write( "b,c,d<BR>\n" );
document.write( "b,c,e<BR>\n" );
document.write( "b,c,f<BR>\n" );
document.write( "b,d,e<BR>\n" );
document.write( "b,d,f<BR>\n" );
document.write( "b,e,f\r<BR>\n" );
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document.write( "total of 3 ways to get 3 women\r<BR>\n" );
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document.write( "c,d,e<BR>\n" );
document.write( "c,d,f<BR>\n" );
document.write( "c,e,f\r<BR>\n" );
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document.write( "remember:\r<BR>\n" );
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document.write( "men are represented by the letters a and b.<BR>\n" );
document.write( "women are represented by the letters c, d, e, and f.\r<BR>\n" );
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document.write( "the probability of getting 1 woman when the number of men is equal to 2 is equal to 12/20.\r<BR>\n" );
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document.write( "the probability of getting 2 women when the number of men is equal to 2 is equal to 4/20.\r<BR>\n" );
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document.write( "the probability of getting 3 women when the number of men is equal to 2 is equal to 4/20\r<BR>\n" );
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document.write( "the total probability is equal to (12 + 4 + 4) / 20 which is equal to 20/20 which is equal to 1, as it should be.\r<BR>\n" );
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document.write( "change the value of n and the probabilities will change.\r<BR>\n" );
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document.write( "the combination formula is calculated as shown in the following example:\r<BR>\n" );
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document.write( "6C3 is equal to (6*5*4) / (3*2*1) which is equal to (5*4) which is equal to 20.\r<BR>\n" );
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document.write( "4C2 is equal to (4*3) / (2*1) which is equal to (2*3) which is equal to 6.\r<BR>\n" );
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document.write( "the general combination formula for getting x elements out of a set of n elements is:\r<BR>\n" );
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document.write( "nCx is equal to n! / ((n-x)! * x!)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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