<PRE><B>Question 1201940</B>
&lt;br&gt;
(a) Total number of 4-digit numbers&lt;br&gt;
There is one restriction: 0 can&#39;t be the first digit&lt;br&gt;
6 choices for the first digit (1 to 6)
6 choices for the second (any of the remaining 6 digits, including 0)
5 choices for the third
4 choices for the fourth&lt;br&gt;
ANSWER for (a): 6*6*5*4 = 720&lt;br&gt;
(b) Number of 4-digit odd numbers&lt;br&gt;
There are two restrictions: 0 can&#39;t be first, and the last digit must be odd.  There are two cases to consider -- first digit odd or first digit even.&lt;br&gt;
(b1) odd; first digit even&lt;br&gt;
3 choices for first digit (2, 4, or 6)
3 choices for the last digit (1, 3, or 5)
5 choices for the second (any of the remaining 5 digits)
4 choices for the third
total: 3*3*5*4 = 180&lt;br&gt;
(b2) odd, first digit odd&lt;br&gt;
3 choices for the first digit (1, 3, or 5)
2 choices for the last (there are only 2 other odd digits)
5 choices for the second (any of the remaining 5 digits)
4 choices for the third
total: 3*2*5*4 = 120&lt;br&gt;
ANSWER for (b): 180+120 = 300&lt;br&gt;
(c) Number greater than 330&lt;br&gt;
ANSWER: 720 (all 4-digit numbers are greater than 330...!)&lt;br&gt;
NOTE: The &quot;330&quot; 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....&lt;br&gt;
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.&lt;br&gt;
Let&#39;s see....&lt;br&gt;
(d1) even, first digit even&lt;br&gt;
3 choices for the first digit (2, 4, or 6)
3 choices for the last digit (any of the three remaining even digits, including 0)
5 choices for the second
4 choices for the third
total: 3*3*5*4 = 180&lt;br&gt;
(d2) even, first digit odd&lt;br&gt;
3 choices for the first digit (1, 3, or 5)
4 choices for the last digit (any of the 4 even digits)
5 choices for the second
4 choices for the third
total: 3*4*5*4 = 240&lt;br&gt;
Total even: 180+240 = 420 CORRECT!&lt;br&gt;
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