document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100100>Question 1100100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When tall and colorful plants are crossed with short and colorless plants, four types of plants will result:  tall and colorful, tall and colorless, short and colorful, and short and colorless with corresponding probabilities:  0.37, 0.42, 0.11, and 0.10.  Ten plants are selected.  \r<BR>\n" );
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document.write( "Find the probability that 5 will be tall and colorful, 2 will be tall and colorless, 2 will be short and colorful, and 1 will be short and colorless. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714579 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=714579\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>Denoting the four types of plants as A, B, C, and D, the \"probability vector\" for each plant is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.37A%2B0.42B%2B0.11C%2B0.10D ALIGN=MIDDLE  ALT=\"0.37A%2B0.42B%2B0.11C%2B0.10D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The probability of selecting 10 plants and getting 5 of A, 2 each of B and C, and 1 of D, is given by the coefficient of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%5E5%29%28B%5E2%29%28C%5E2%29%28D%5E1%29 ALIGN=MIDDLE  ALT=\"%28A%5E5%29%28B%5E2%29%28C%5E2%29%28D%5E1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > term in the expansion of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.37A%2B0.42B%2B0.11C%2B0.10D%29%5E10 ALIGN=MIDDLE  ALT=\"%280.37A%2B0.42B%2B0.11C%2B0.10D%29%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "While the actual computation is ugly, the multinomial formula gives us the required calculation:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2810%21%29%2F%28%285%21%29%282%21%29%282%21%29%281%21%29%29%29%2A%280.37%5E5%29%280.42%5E2%29%280.11%5E2%29%280.10%5E1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "I'll let you crunch the numbers.... </SPAN>\n" );
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