document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039942>Question 1039942</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group consists of seven men and eight women. Three people are selected to attend a conference.<BR>\n" );
document.write( "a. In how many ways can three people be selected from this group of fifteen?<BR>\n" );
document.write( "b. In how many ways can three women be selected from the eight &#8203;women?<BR>\n" );
document.write( "c. Find the probability that the selected group will consist of all women. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #654708 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=654708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part A) In how many ways can three people be selected from this group of fifteen?\r<BR>\n" );
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document.write( "There are 15 people total. We want to select 3 of them.\r<BR>\n" );
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document.write( "n = 15<BR>\n" );
document.write( "r = 3\r<BR>\n" );
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document.write( "Use the <a  rel=nofollow HREF=\"http://www.mathwords.com/c/combination_formula.htm\">combination formula</a> to get\r<BR>\n" );
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document.write( "n C r = (n!)/(r!(n-r)!)\r<BR>\n" );
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document.write( "15 C 3 = (15!)/(3!*(15-3)!)\r<BR>\n" );
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document.write( "15 C 3 = (15!)/(3!*12!)\r<BR>\n" );
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document.write( "15 C 3 = (15*14*13*12!)/(3!*12!)\r<BR>\n" );
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document.write( "15 C 3 = (15*14*13)/(3!)\r<BR>\n" );
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document.write( "15 C 3 = (15*14*13)/(3*2*1)\r<BR>\n" );
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document.write( "15 C 3 = (2730)/(6)\r<BR>\n" );
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document.write( "15 C 3 = 455\r<BR>\n" );
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document.write( "Part B) In how many ways can three women be selected from the eight women?\r<BR>\n" );
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document.write( "There are 8 women and we want to choose 3 of them.\r<BR>\n" );
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document.write( "Similar to part A, we use the combination formula with n = 8 and r = 3\r<BR>\n" );
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document.write( "n C r = (n!)/(r!(n-r)!)\r<BR>\n" );
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document.write( "8 C 3 = (8!)/(3!*(8-3)!)\r<BR>\n" );
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document.write( "8 C 3 = (8!)/(3!*5!)\r<BR>\n" );
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document.write( "8 C 3 = (8*7*6*5!)/(3!*5!)\r<BR>\n" );
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document.write( "8 C 3 = (8*7*6)/(3!)\r<BR>\n" );
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document.write( "8 C 3 = (8*7*6)/(3*2*1)\r<BR>\n" );
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document.write( "8 C 3 = (336)/(6)\r<BR>\n" );
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document.write( "8 C 3 = 56\r<BR>\n" );
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document.write( "Part C) Find the probability that the selected group will consist of all women.\r<BR>\n" );
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document.write( "Divide the two values from parts A and B to get...\r<BR>\n" );
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document.write( "(result from part B)/(result from part A) = (# of ways to pick 3 women)/(# of ways to pick 3 people)\r<BR>\n" );
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document.write( "(result from part B)/(result from part A) = 56/455\r<BR>\n" );
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document.write( "(result from part B)/(result from part A) = 0.12307692307692\r<BR>\n" );
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document.write( "This is approximate.\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "Answer to part A: <font color=red>455</font><BR>\n" );
document.write( "Answer to part B: <font color=red>56</font><BR>\n" );
document.write( "Answer to part C: <font color=red>0.12307692307692</font>\r<BR>\n" );
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document.write( "The result for part C is approximate. <BR>\n" );
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