document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037064>Question 1037064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a baby shower, 15 guests are in attendance and 3 of them are randomly selected to receive a door prize.<BR>\n" );
document.write( "Question: If all 5 prizes are different, in how many ways can the prizes be awarded?<BR>\n" );
document.write( "I came up with 5x5x5=125 or 5^3 am I doing this right? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #651760 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=651760\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> probably not.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 prizes being given to 3 people.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "presumably each person will be given only 1 prize.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in that case, then 5C3 sound like the correct formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5C3 = 5! / (3! * 2!) = (5*4*3!) / (3!*2!) = (5*4)/2!= (5*4)/2 = 10.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "there are 10 ways that 3 people can each receive 1 out of 5 possible prizes.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let's assume the prizes are a,b,c,d,e.<BR>\n" );
document.write( "that's 5 in total.<BR>\n" );
document.write( "1 prize will be given to each of 3 people.<BR>\n" );
document.write( "the possible ways that each of 3 people can receive the prizes would be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a,b,c<BR>\n" );
document.write( "a,b,d<BR>\n" );
document.write( "a,b,e<BR>\n" );
document.write( "a,c,d<BR>\n" );
document.write( "a,c,e<BR>\n" );
document.write( "a,d,e<BR>\n" );
document.write( "b,c,d<BR>\n" );
document.write( "b,c,e<BR>\n" );
document.write( "b,d,e<BR>\n" );
document.write( "c,d,e\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a,b,c means that person 1 gets a, person 2 gets b, person 3 gets c.<BR>\n" );
document.write( "a,b,d means that person 1 gets a, person 2 gets b, person 3 gets d.<BR>\n" );
document.write( "etc.....\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5*5*5 doesn't work because then you have the possibility that more than 1 person can get the same prize at the same time, which is impossible.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );