document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=504398>Question 504398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> to win a lotto in one state, one must correctly select 6 numbers from a collection of 46 numbers. the order does not matter. How many different selections are possible </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339602 by </B><A HREF=/tutors/aboutme.mpl?userid=Maths68><B>Maths68(1474)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Maths68><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=Maths68><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=339602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If order does not matter then we can use following formula to find different COMBINATIONS of 6 numbers out of 46 numbers\r<BR>\n" );
document.write( "\n" );
document.write( "Use following Combination formula<BR>\n" );
document.write( "nCr = n! / r!(n-r)!<BR>\n" );
document.write( "n=46<BR>\n" );
document.write( "r=6<BR>\n" );
document.write( "=46!/6!(46-6)!<BR>\n" );
document.write( "=46!/[6!(40)!]<BR>\n" );
document.write( "=(46*45*44*43*42*41*40!)/(6*5*4*3*2*1)(40!)<BR>\n" );
document.write( "Cancel out 40!<BR>\n" );
document.write( "=46*45*44*43*42*41/(6*5*4*3*2*1)<BR>\n" );
document.write( "=6744109680/720<BR>\n" );
document.write( "=9366819<BR>\n" );
document.write( "Possible different selection 9366819 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );