document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193831>Question 1193831</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a race between 7 horses how many ways can the first 3 horses show? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825863 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=825863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: 210\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Reason:<BR>\n" );
document.write( "There are 7 ways to select first place<BR>\n" );
document.write( "Then 7-1 = 6 ways to get second place<BR>\n" );
document.write( "And 7-2 = 5 ways to get third place\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Overall there are 7*6*5 = 210 ways to finish the race\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We could use the nPr formula as an alternative path<BR>\n" );
document.write( "n = 7 and r = 3<BR>\n" );
document.write( "n P r = (n!)/( (n-r)! )<BR>\n" );
document.write( "7 P 3 = (7!)/( (7-3)! )<BR>\n" );
document.write( "7 P 3 = (7!)/( 4! )<BR>\n" );
document.write( "7 P 3 = (7*6*5*4!)/( 4! )<BR>\n" );
document.write( "7 P 3 = 7*6*5<BR>\n" );
document.write( "7 P 3 = 210<BR>\n" );
document.write( "On the second to last line, the \"4!\" terms canceled and we have the string \"7*6*5\" show up again. <BR>\n" );
document.write( "If you wanted, you can expand out the 4! to get 4*3*2*1, but they cancel out anyway.<BR>\n" );
document.write( "Order matters when it comes to the 1st,2nd,3rd place positions. This is why we use nPr instead of nCr.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Some calculators have a specialized nPr button or feature buried inside them somewhere. <BR>\n" );
document.write( "On the TI83 for instance, you hit the button labeled \"MATH\" (unfortunately a very poor choice of naming since everything on a calculator pertains to math) and scroll over to the \"PRB\" submenu. Then scroll down to nPr. You'll need to type the 7 first before putting the 'nPr' to your home screen. Then type 3 to finish things up and 210 should result.<BR>\n" );
document.write( "So you should have 7 nPr 3 on one line and then it results in 210 on the next line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you don't have a calculator like a TI83, then you can use a free online one such as this <BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.calculatorsoup.com/calculators/discretemathematics/permutations.php\">https://www.calculatorsoup.com/calculators/discretemathematics/permutations.php</a><BR>\n" );
document.write( "I recommend to use it to check your work rather than do everything for you. You won't get practice if you let a machine do all the work. <BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );