document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170425>Question 170425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the problem. \r<BR>\n" );
document.write( "\n" );
document.write( "Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw all black cards?\r<BR>\n" );
document.write( "\n" );
document.write( "a. 32,890<BR>\n" );
document.write( "b. 263,120<BR>\n" );
document.write( "c. 65,780<BR>\n" );
document.write( "d. 131,560 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125825 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=125825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 26 black cards (13 spade and 13 club cards) to choose from. So this means that n=26. Since the amount per hand is 5 cards, this means that r=5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since order does not matter, we must use the <a  rel=nofollow HREF=http://www.mathwords.com/c/combination_formula.htm>combination formula</a>:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{n}C_{r}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-r%29%21r%21 ALIGN=MIDDLE  ALT=\"n%21%2F%28n-r%29%21r%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{26}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%21%2F%2826-5%29%215%21 ALIGN=MIDDLE  ALT=\"26%21%2F%2826-5%29%215%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=26 ALIGN=MIDDLE  ALT=\"n=26\"   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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{26}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%21%2F21%215%21 ALIGN=MIDDLE  ALT=\"26%21%2F21%215%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26-5 ALIGN=MIDDLE  ALT=\"26-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 21\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand 26!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{26}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2826%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%2F21%215%21 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand 21!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{26}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2826%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%2821%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%295%21 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{26}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2826%2A25%2A24%2A23%2A22%2Across%2821%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%29%2F%28cross%2821%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%295%21 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  Cancel\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{26}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2826%2A25%2A24%2A23%2A22%29%2F5%21 ALIGN=MIDDLE  ALT=\"%2826%2A25%2A24%2A23%2A22%29%2F5%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand 5!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{26}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2826%2A25%2A24%2A23%2A22%29%2F%285%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%2826%2A25%2A24%2A23%2A22%29%2F%285%2A4%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{26}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7893600%2F%285%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"7893600%2F%285%2A4%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply 26*25*24*23*22 to get 7,893,600\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{26}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7893600%2F120 ALIGN=MIDDLE  ALT=\"7893600%2F120\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 5*4*3*2*1 to get 120\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{26}C_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65780 ALIGN=MIDDLE  ALT=\"65780\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So 26 choose 5 (where order doesn't matter) yields 65,780 unique combinations\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So there are 65,780 possible ways to choose all black cards.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );