document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912625>Question 912625</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are five people in my family. How many different groupings of these five people can be formed (i.e. groups with from 1 to 5 members)?\r<BR>\n" );
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document.write( "I know the answer is 31, but is there a formula for solving this? (Not homework, just a problem I thought of, and can't find a method on the internet!)\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553931 by </B><A HREF=/tutors/aboutme.mpl?userid=ichigo449><B>ichigo449(30)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ichigo449><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=553931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are dealing with combinations, or the number of ways of arranging, in an ordered fashion, k objects from a set with n total objects and is defined as n!/k!(n-k)!. Where x! is the factorial function. Your answer is the addition of each combination running from 1 to 5.   </SPAN>\n" );
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