document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158401>Question 1158401</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find how many distinct numbers greater than 5000 and divisible by 3 can be formed from the digits 3,4,5,6 and 0, if each digit is used atmost once in a number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781436 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=781436\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Edwin's solution is good, as usual.<br><BR>\n" );
document.write( "Here is another approach, to show you there is almost always more than one way to analyze a problem.<br><BR>\n" );
document.write( "The sum of the five given digits is 18, which is divisible by 3.  Since all 5-digit numbers are greater than 5000, every 5-digit number that can be formed with these digits satisfies the requirements.<br><BR>\n" );
document.write( "The first digit can't be 0; so we can choose...<BR>\n" );
document.write( "the first digit 4 ways;<BR>\n" );
document.write( "the second digit 4 ways;<BR>\n" );
document.write( "the third digit 3 ways;<BR>\n" );
document.write( "the fourth digit 2 ways; and<BR>\n" );
document.write( "the fifth digit 1 way.<br><BR>\n" );
document.write( "Number of 5-digit numbers we can make: 4*4*3*2*1 = 96.<br><BR>\n" );
document.write( "For 4-digit numbers, the first digit must be either 5 or 6 if the number is going to be greater than 5000.<br><BR>\n" );
document.write( "4-digit numbers with first digit 6....<br><BR>\n" );
document.write( "With first digit 6, for the sum of the digits to be divisible by 3, the digits 4 and 5 must both be used.  So we must use both of those digits and choose one of the remaining two digits; then those last three digits can be arranged in 3!=6 different ways.<br><BR>\n" );
document.write( "Number of 4-digit numbers with leading digit 6: 2*6 = 12.<br><BR>\n" );
document.write( "4-digit numbers with first digit 5....<br><BR>\n" );
document.write( "With first digit 5, for the sum of the digits to be divisible by 3, the digit 4 must also be used.  So we use the 4, and we choose 2 of the remaining 3 digits.  We can choose 2 of the remaining three digits is C(3,2)=3 ways; then those last three digits can be arranged in 3!=6 different ways.<br><BR>\n" );
document.write( "Number of 4-digit numbers with leading digit 6: 3*6 = 18.<br><BR>\n" );
document.write( "Total number of numbers we can form: 96+12+18 = 126.<br><BR>\n" );
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