document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144816>Question 1144816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student number system for a county requires that the student number be 5 characters. The first 3 characters are any single digit number, but no number can repeat and the last 2 characters must be letters, but no letter can repeat. How many unique student numbers are possible?\r<BR>\n" );
document.write( "\n" );
document.write( "A. 1,370\r<BR>\n" );
document.write( "\n" );
document.write( "B. 131,040\r<BR>\n" );
document.write( "\n" );
document.write( "C. 250,000\r<BR>\n" );
document.write( "\n" );
document.write( "D. 468,000\r<BR>\n" );
document.write( "\n" );
document.write( "Is D correct?\r<BR>\n" );
document.write( "\n" );
document.write( "The question and the answer choices in the link here: https://prnt.sc/p3ubbd </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #765987 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=765987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "We have 5 slots to fill. Let's call them A,B,C,D,E\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first three slots (A,B,C) are a single digit number. We have 10 choices for slot A, 9 for B, and 8 for C. So far we have 10*9*8 = 720 different ways to form a three digit number where the digits do not repeat. It's possible to select 0 first. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For slot D, we have 26 letters to pick from. For slot E, we have 25 letters left over. So we have 26*25 = 650 different two letter combos (repeat not allowed)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply the two sub-results and we end up with: 720*650 = 468,000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Choice D is the correct answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As shorthand you can simply multiply everything out as such<BR>\n" );
document.write( "10*9*8*26*25 = 468,000<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );