document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88973>Question 88973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is your probability of winning the lottery if the balls number 1 to 54 and you have to get correct?  The order in which the selection is made dont matter.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64672 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=64672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You didn't say how many balls are selected. Lets say you choose 5 balls, and since order doesn't matter, we can use the combination formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{n}C_{r}=\frac{n!}{(n-r)!r!}}\"> Start with the given formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{54}C_{5}=\frac{54!}{(54-5)!5!}}\"> Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=54 ALIGN=MIDDLE  ALT=\"n=54\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=5 ALIGN=MIDDLE  ALT=\"r=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{54}C_{5}=\frac{54!}{49!5!}}\"> Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54-5 ALIGN=MIDDLE  ALT=\"54-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 49\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{54}C_{5}\">=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2854%2A53%2A52%2A51%2A50%2A49%2A48%2A47%2A46%2A45%2A44%2A43%2A42%2A41%2A40%2A39%2A38%2A37%2A36%2A35%2A34%2A33%2A32%2A31%2A30%2A29%2A28%2A27%2A26%2A25%2A24%2A23%2A22%2A21%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%2849%215%21%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Expand 54!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{54}C_{5}\">=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2854%2A53%2A52%2A51%2A50%2A49%2A48%2A47%2A46%2A45%2A44%2A43%2A42%2A41%2A40%2A39%2A38%2A37%2A36%2A35%2A34%2A33%2A32%2A31%2A30%2A29%2A28%2A27%2A26%2A25%2A24%2A23%2A22%2A21%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%28%2849%2A48%2A47%2A46%2A45%2A44%2A43%2A42%2A41%2A40%2A39%2A38%2A37%2A36%2A35%2A34%2A33%2A32%2A31%2A30%2A29%2A28%2A27%2A26%2A25%2A24%2A23%2A22%2A21%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%295%21%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Expand 49!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{54}C_{5}\">=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2854%2A53%2A52%2A51%2A50%2Across%2849%2A48%2A47%2A46%2A45%2A44%2A43%2A42%2A41%2A40%2A39%2A38%2A37%2A36%2A35%2A34%2A33%2A32%2A31%2A30%2A29%2A28%2A27%2A26%2A25%2A24%2A23%2A22%2A21%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%29%2F%28%28cross%2849%2A48%2A47%2A46%2A45%2A44%2A43%2A42%2A41%2A40%2A39%2A38%2A37%2A36%2A35%2A34%2A33%2A32%2A31%2A30%2A29%2A28%2A27%2A26%2A25%2A24%2A23%2A22%2A21%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%295%21%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{54}C_{5}\">=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2854%2A53%2A52%2A51%2A50%29%2F5%21%29 ALIGN=MIDDLE  ALT=\"%2854%2A53%2A52%2A51%2A50%29%2F5%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{54}C_{5}\frac{379501200}{5!}\"> Calculate 54*53*52*51*50 to get 379,501,200\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{54}C_{5}=\frac{379501200}{120}\"> Calculate 5! to get 120\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{54}C_{5}=\frac{379501200}{120}}\"> Multiply the values in the denominator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{54}C_{5}=3162510\"> Divide \r<BR>\n" );
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document.write( "So 54 choose 5 (where order does not matter) yields 3,162,510 unique combinations\r<BR>\n" );
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document.write( "So the probability of winning is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3162510 ALIGN=MIDDLE  ALT=\"1%2F3162510\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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