document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193916>Question 1193916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many different four-digit numbers are possible if each digit of the number is either 0,1,2,3,4 or 5, and numbers starting with 3 cannot be even?\r<BR>\n" );
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document.write( "The textbook answer is 972.\r<BR>\n" );
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document.write( "Can someone tell me how to solve this problem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825978 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The first digit can't be 0; and there are special requirements if the first digit is 3.  So consider two cases -- first digit 1, 2, 4, or 5; or first digit 3.<br><BR>\n" );
document.write( "(1) first digit 1, 2, 4, or 5<br><BR>\n" );
document.write( "There are 4 choices for that first digit, then there are no restrictions for the other digits; so the number of 4-digit numbers with first digit 1, 2, 4, or 5 is 4*6*6*6=864.<br><BR>\n" );
document.write( "(2) first digit 3<br><BR>\n" );
document.write( "The first digit has to be 3 (1 choice); the last digit must be odd (1, 3, or 5 -- 3 choices); and there are no restrictions on the other two digits.  The number of possible 4-digit even numbers with first digit 3 is 1*3*6*6=108.<br><BR>\n" );
document.write( "The total number of 4-digit numbers with the given requirements is 864+108=972.<br><BR>\n" );
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document.write( "A comment for tutor @ikleyn, whose math is nearly always very good but whose English is often not....<br><BR>\n" );
document.write( "There is nothing deficient in the statement of the problem.  It says that \"each digit of the number is either 0,1,2,3,4 or 5\".  That means repetition of digits is allowed.<br><BR>\n" );
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