document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143040>Question 143040</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag contains 15 billiard balls, numbers consecutively from 1 to 15. Six balls are selected at random. What is the probability that the sum of the numbers on the billiard balls will be odd? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104095 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=104095\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 8 are odd, 7 are even.<BR>\n" );
document.write( "All the possible combinations are:<BR>\n" );
document.write( "8C6=28 [all odd]<BR>\n" );
document.write( "8C5 * 7C1 =56*7=392 [5 odd, 1 even]<BR>\n" );
document.write( "8C4 * 7C2 =70*21=1470 [4 odd, 2 even]<BR>\n" );
document.write( "8C3 * 7C3 =56*35=1960 [3 odd, 3 even]<BR>\n" );
document.write( "8C2 * 7C4 =28*35=980 [2 odd, 4 even]<BR>\n" );
document.write( "8C1 * 7C5 =8*21=168 [1 odd, 5 even]<BR>\n" );
document.write( "7C6=7 [all even]<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Adding all these numbers we get 5005 possible combinations.<BR>\n" );
document.write( "Only those with an odd number of odd numbers give an odd result.<BR>\n" );
document.write( "They are: 392+1960+168=2520<BR>\n" );
document.write( "2520/5005=72/143 or .503497 Probability that the sum of the numbers will be odd.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );