document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=35742>Question 35742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <i><b> Determine the number of possible outcomes and please show work</i></b>\r<BR>\n" );
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document.write( "How many ways can 6 items be selected for a gift basket from twelve possible items if the order of selection does not matter?\r<BR>\n" );
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document.write( "Thanks so much!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #21853 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=21853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a combination problem, since the order of selection does NOT matter.  The number of ways of choosing 6 items from 12 is called a C(12, 6).  There is a formula that a lot of people use, but I think it's easier to do it this way.\r<BR>\n" );
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document.write( "If it had been a permutation (in which the order DID matter), then it would be a P(12,6).  With a P(12,6), start with 12*11*10*9*8*7 and multiply these 6 numbers together.  If it had been P(12, 2), then the answer is 12*11.  In other words the first number tells you where to start counting down, and the second number tells you how many numbers to multiply.\r<BR>\n" );
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document.write( "Now, the difference between a Combination and a Permutation is that with a Combination, you must multiply the same numbers as for a permutation, but divide by the factorial of the second number.  Here are some examples of combinations:<BR>\n" );
document.write( "C(5,2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%29%2F%282%2A1%29=+5%2A2=+10 ALIGN=MIDDLE  ALT=\"%285%2A4%29%2F%282%2A1%29=+5%2A2=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "C(6,2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2A5%29%2F%282%2A1%29=+3%2A5=+15 ALIGN=MIDDLE  ALT=\"%286%2A5%29%2F%282%2A1%29=+3%2A5=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "C(12,2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A11%29%2F%282%2A1%29=+6%2A11=+66 ALIGN=MIDDLE  ALT=\"%2812%2A11%29%2F%282%2A1%29=+6%2A11=+66\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "C(5,3) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%2A3%29%2F%283%2A2%2A1%29=+60%2F6=+10 ALIGN=MIDDLE  ALT=\"%285%2A4%2A3%29%2F%283%2A2%2A1%29=+60%2F6=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now here at last is YOUR question:<BR>\n" );
document.write( "C(12,6)= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A11%2A10%2A9%2A8%2A7%29%2F%286%2A5%2A4%2A3%2A2%2A1%29+ ALIGN=MIDDLE  ALT=\"%2812%2A11%2A10%2A9%2A8%2A7%29%2F%286%2A5%2A4%2A3%2A2%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Got a calculator???  I got 924 for the answer.  By the way, most of your calculators, even a $15 TI 30 will do this for you, so you don't have to understand this lesson!!\r<BR>\n" );
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document.write( "R^2 at SCC <BR>\n" );
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