document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200086>Question 1200086</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Five fair coins were tossed simultaneously. What is the probability of getting three heads and two tails?<BR>\n" );
document.write( "A. 1/32 <BR>\n" );
document.write( "B. 1/16<BR>\n" );
document.write( "C. 1/8<BR>\n" );
document.write( "D. 1/4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834113 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=834113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The wording of the problem most definitely does NOT say the 5 outcomes are 3 heads followed by 2 tails in that order....<br><BR>\n" );
document.write( "The number of possible outcomes on 5 flips of the coin is 2^5 = 32.<br><BR>\n" );
document.write( "The number of ways (different orders) of getting 3 heads and 2 tails is the number of different ways of arranging the letters HHHTT.  By a well-known counting principle, that number of ways is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%21%29%2F%28%283%21%29%282%21%29%29=120%2F12=10 ALIGN=MIDDLE  ALT=\"%285%21%29%2F%28%283%21%29%282%21%29%29=120%2F12=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "So the probability of getting 3 heads and 2 tails is 10/32 = 5/16.<br><BR>\n" );
document.write( "Note for problems involving flipping fair coins, a familiarity with Pascal's Triangle is helpful.  The 5th row of Pascal's Triangle is<br><BR>\n" );
document.write( "1 5 10 10 5 1<br><BR>\n" );
document.write( "Those numbers represent, respectively, the numbers of different ways of getting 5, 4, 3, 2, 1, or 0 heads.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );