document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201940>Question 1201940</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many four-digit numbers can be formed from the digits 0, 1,2,3,4,5,and 6 if each digit can be used only once?<BR>\n" );
document.write( "(b) How many of these are odd numbers?<BR>\n" );
document.write( "(c)How many are greater than 330? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836530 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=836530\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(a) Total number of 4-digit numbers<br><BR>\n" );
document.write( "There is one restriction: 0 can't be the first digit<br><BR>\n" );
document.write( "6 choices for the first digit (1 to 6)<BR>\n" );
document.write( "6 choices for the second (any of the remaining 6 digits, including 0)<BR>\n" );
document.write( "5 choices for the third<BR>\n" );
document.write( "4 choices for the fourth<br><BR>\n" );
document.write( "ANSWER for (a): 6*6*5*4 = 720<br><BR>\n" );
document.write( "(b) Number of 4-digit odd numbers<br><BR>\n" );
document.write( "There are two restrictions: 0 can't be first, and the last digit must be odd.  There are two cases to consider -- first digit odd or first digit even.<br><BR>\n" );
document.write( "(b1) odd; first digit even<br><BR>\n" );
document.write( "3 choices for first digit (2, 4, or 6)<BR>\n" );
document.write( "3 choices for the last digit (1, 3, or 5)<BR>\n" );
document.write( "5 choices for the second (any of the remaining 5 digits)<BR>\n" );
document.write( "4 choices for the third<BR>\n" );
document.write( "total: 3*3*5*4 = 180<br><BR>\n" );
document.write( "(b2) odd, first digit odd<br><BR>\n" );
document.write( "3 choices for the first digit (1, 3, or 5)<BR>\n" );
document.write( "2 choices for the last (there are only 2 other odd digits)<BR>\n" );
document.write( "5 choices for the second (any of the remaining 5 digits)<BR>\n" );
document.write( "4 choices for the third<BR>\n" );
document.write( "total: 3*2*5*4 = 120<br><BR>\n" );
document.write( "ANSWER for (b): 180+120 = 300<br><BR>\n" );
document.write( "(c) Number greater than 330<br><BR>\n" );
document.write( "ANSWER: 720 (all 4-digit numbers are greater than 330...!)<br><BR>\n" );
document.write( "NOTE: The \"330\" in the post is probably a typo; it was probably supposed to be a 4-digit number.  So this was probably supposed to be a much more interesting problem -- but I am answering the question that was asked in the post....<br><BR>\n" );
document.write( "NOTE: For a student just learning to work problems like this, it is a useful exercise to calculate how many of these 4-digit numbers are even.  Since there are a total of 720 numbers, of which 300 are odd, there should be 420 that are even.<br><BR>\n" );
document.write( "Let's see....<br><BR>\n" );
document.write( "(d1) even, first digit even<br><BR>\n" );
document.write( "3 choices for the first digit (2, 4, or 6)<BR>\n" );
document.write( "3 choices for the last digit (any of the three remaining even digits, including 0)<BR>\n" );
document.write( "5 choices for the second<BR>\n" );
document.write( "4 choices for the third<BR>\n" );
document.write( "total: 3*3*5*4 = 180<br><BR>\n" );
document.write( "(d2) even, first digit odd<br><BR>\n" );
document.write( "3 choices for the first digit (1, 3, or 5)<BR>\n" );
document.write( "4 choices for the last digit (any of the 4 even digits)<BR>\n" );
document.write( "5 choices for the second<BR>\n" );
document.write( "4 choices for the third<BR>\n" );
document.write( "total: 3*4*5*4 = 240<br><BR>\n" );
document.write( "Total even: 180+240 = 420 CORRECT!<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );