document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083149>Question 1083149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is r if 9Pr= 3024<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697162 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=697162\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's compute the following ten nPr values. <BR>\n" );
document.write( "Fix n = 9 (ie don't change this value)<BR>\n" );
document.write( "Let r be a whole number and let it range from r = 0 to r = 9.<BR>\n" );
document.write( "The goal is to find which r value yields n P r = 9 P r = 3024.\r<BR>\n" );
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document.write( "When r = 0, then...\r<BR>\n" );
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document.write( "n P r = (n!)/((n-r)!)<BR>\n" );
document.write( "9 P 0 (9!)/((9-0)!)<BR>\n" );
document.write( "9 P 0 = (9!)/(9!)<BR>\n" );
document.write( "9 P 0 = (9*8*7*6*5*4*3*2*1)/(9*8*7*6*5*4*3*2*1)<BR>\n" );
document.write( "9 P 0 = (362880)/(362880)<BR>\n" );
document.write( "9 P 0 = 1\r<BR>\n" );
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document.write( "When r = 1, then...\r<BR>\n" );
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document.write( "n P r = (n!)/((n-r)!)<BR>\n" );
document.write( "9 P 1 (9!)/((9-1)!)<BR>\n" );
document.write( "9 P 1 = (9!)/(8!)<BR>\n" );
document.write( "9 P 1 = (9*8*7*6*5*4*3*2*1)/(8*7*6*5*4*3*2*1)<BR>\n" );
document.write( "9 P 1 = (362880)/(40320)<BR>\n" );
document.write( "9 P 1 = 9\r<BR>\n" );
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document.write( "When r = 2, then...\r<BR>\n" );
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document.write( "n P r = (n!)/((n-r)!)<BR>\n" );
document.write( "9 P 2 (9!)/((9-2)!)<BR>\n" );
document.write( "9 P 2 = (9!)/(7!)<BR>\n" );
document.write( "9 P 2 = (9*8*7*6*5*4*3*2*1)/(7*6*5*4*3*2*1)<BR>\n" );
document.write( "9 P 2 = (362880)/(5040)<BR>\n" );
document.write( "9 P 2 = 72\r<BR>\n" );
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document.write( "When r = 3, then...\r<BR>\n" );
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document.write( "n P r = (n!)/((n-r)!)<BR>\n" );
document.write( "9 P 3 (9!)/((9-3)!)<BR>\n" );
document.write( "9 P 3 = (9!)/(6!)<BR>\n" );
document.write( "9 P 3 = (9*8*7*6*5*4*3*2*1)/(6*5*4*3*2*1)<BR>\n" );
document.write( "9 P 3 = (362880)/(720)<BR>\n" );
document.write( "9 P 3 = 504\r<BR>\n" );
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document.write( "When r = 4, then...\r<BR>\n" );
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document.write( "n P r = (n!)/((n-r)!)<BR>\n" );
document.write( "9 P 4 (9!)/((9-4)!)<BR>\n" );
document.write( "9 P 4 = (9!)/(5!)<BR>\n" );
document.write( "9 P 4 = (9*8*7*6*5*4*3*2*1)/(5*4*3*2*1)<BR>\n" );
document.write( "9 P 4 = (362880)/(120)<BR>\n" );
document.write( "9 P 4 = 3024\r<BR>\n" );
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document.write( "When r = 5, then...\r<BR>\n" );
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document.write( "n P r = (n!)/((n-r)!)<BR>\n" );
document.write( "9 P 5 (9!)/((9-5)!)<BR>\n" );
document.write( "9 P 5 = (9!)/(4!)<BR>\n" );
document.write( "9 P 5 = (9*8*7*6*5*4*3*2*1)/(4*3*2*1)<BR>\n" );
document.write( "9 P 5 = (362880)/(24)<BR>\n" );
document.write( "9 P 5 = 15120\r<BR>\n" );
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document.write( "When r = 6, then...\r<BR>\n" );
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document.write( "n P r = (n!)/((n-r)!)<BR>\n" );
document.write( "9 P 6 (9!)/((9-6)!)<BR>\n" );
document.write( "9 P 6 = (9!)/(3!)<BR>\n" );
document.write( "9 P 6 = (9*8*7*6*5*4*3*2*1)/(3*2*1)<BR>\n" );
document.write( "9 P 6 = (362880)/(6)<BR>\n" );
document.write( "9 P 6 = 60480\r<BR>\n" );
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document.write( "When r = 7, then...\r<BR>\n" );
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document.write( "n P r = (n!)/((n-r)!)<BR>\n" );
document.write( "9 P 7 (9!)/((9-7)!)<BR>\n" );
document.write( "9 P 7 = (9!)/(2!)<BR>\n" );
document.write( "9 P 7 = (9*8*7*6*5*4*3*2*1)/(2*1)<BR>\n" );
document.write( "9 P 7 = (362880)/(2)<BR>\n" );
document.write( "9 P 7 = 181440\r<BR>\n" );
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document.write( "When r = 8, then...\r<BR>\n" );
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document.write( "n P r = (n!)/((n-r)!)<BR>\n" );
document.write( "9 P 8 (9!)/((9-8)!)<BR>\n" );
document.write( "9 P 8 = (9!)/(1!)<BR>\n" );
document.write( "9 P 8 = (9*8*7*6*5*4*3*2*1)/(1)<BR>\n" );
document.write( "9 P 8 = (362880)/(1)<BR>\n" );
document.write( "9 P 8 = 362880\r<BR>\n" );
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document.write( "When r = 9, then...\r<BR>\n" );
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document.write( "n P r = (n!)/((n-r)!)<BR>\n" );
document.write( "9 P 9 (9!)/((9-9)!)<BR>\n" );
document.write( "9 P 9 = (9!)/(0!)<BR>\n" );
document.write( "9 P 9 = (9*8*7*6*5*4*3*2*1)/(1)<BR>\n" );
document.write( "9 P 9 = (362880)/(1)<BR>\n" );
document.write( "9 P 9 = 362880\r<BR>\n" );
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document.write( "In the work shown above, we see that 9 P 4 = 3024\r<BR>\n" );
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document.write( "So if 9 P r = 3024, then r = 4\r<BR>\n" );
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document.write( "Answer: <font color=red>4</font> </SPAN>\n" );
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