document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=595250>Question 595250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Toss a penny, nickel, dime and quarter together. How many heads/tails arrangements are possible? Of those, how many have two heads and two tails?\r<BR>\n" );
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document.write( "My attempts:<BR>\n" );
document.write( "(2C1)*(2C1)*(2C1)*(2C1)=16 possible combinations<BR>\n" );
document.write( "How can I find out how many combinations have 2 head and 2 tails? Am I on the right track? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377050 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=377050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are correct. There are 16 possible outcomes.\r<BR>\n" );
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document.write( "Of these 16 outcomes, only the following have two heads and two tails\r<BR>\n" );
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document.write( "HHTT<BR>\n" );
document.write( "HTHT<BR>\n" );
document.write( "HTTH\r<BR>\n" );
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document.write( "THHT<BR>\n" );
document.write( "THTH<BR>\n" );
document.write( "TTHH\r<BR>\n" );
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document.write( "So there are 6 combinations that have 2 heads and two tails.\r<BR>\n" );
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document.write( "Another way to calculate the above is to notice that there is only way to get all heads HHHH and only one way to get all tails TTTT. So we can subtract these two cases off\r<BR>\n" );
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document.write( "We're left with 16 - 2 = 14 cases\r<BR>\n" );
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document.write( "There are 4 ways to have exactly one head (one for each slot). They are: HTTT, THTT, TTHT, TTTH\r<BR>\n" );
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document.write( "Likewise, there are 4 ways to have exactly one tail, and they are: THHH, HTHH, HHTH, HHHT\r<BR>\n" );
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document.write( "So there are now 14 - 4 - 4 = 6 cases left\r<BR>\n" );
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document.write( "But the only possible outcome is to have 2 heads and 2 tails. This is because having 3 heads leads to one tail or having 3 tails leads to one head.\r<BR>\n" );
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document.write( "So we're led to the same answer of 6. </SPAN>\n" );
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