document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140181>Question 1140181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Classify the problem as a permutation, a combination, or neither.\r<BR>\n" );
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document.write( "In how many ways can two hearts be drawn from a deck of cards? (Order is not important.)\r<BR>\n" );
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document.write( "As well as answer the question.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760687 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=760687\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> :<BR>\n" );
document.write( "order is not important implies combination<BR>\n" );
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document.write( "I will show you two methods for solving this problem<BR>\n" );
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document.write( "Method 1 using combination and probability<BR>\n" );
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document.write( "52C2 = 52!/(2! * (52-2)!) = 1326 ways to select 2 cards out of 52<BR>\n" );
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document.write( "the probability(P) that the first card is a heart is 13/52 = 1/4<BR>\n" );
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document.write( "the P that the second card is a heart is 12/51<BR>\n" );
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document.write( "the P that both are hearts = 1/4 * 12/51 = 0.058823529<BR>\n" );
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document.write( "multiply the P that both are hearts times the ways to select 2 cards out of 52<BR>\n" );
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document.write( "0.058823529 * 1326 = 78 ways two hearts can be drawn from a deck of cards when order is not important<BR>\n" );
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document.write( "Method 2 using selection process and combination<BR>\n" );
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document.write( "13 * 12 = 156 ways to select two hearts<BR>\n" );
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document.write( "since order is not important, we have to divide 156 by 2 - the reason for this is that there are 2 ways for each set of 2 hearts, for example, (4,5) and (5,4) were counted in the above calculation<BR>\n" );
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document.write( "156/2 = 78 ways two hearts can be drawn from a deck of cards when order is not important<BR>\n" );
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