Question 1193916
<pre>

First let's calculate how many 4-digit numbers have digits from
{0,1,2,3,4,5}, 
regardless of whether they start with 3 or are odd or even.  Then 
we'll calculate how many start with 3 and are even, and subtract. 

A. Since a 4-digit number can't start with 0, the ways to 
choose the 1st digit are any one of these: {1,2,3,4,5}.  
How many choices is that? _____

B. The ways to choose the 2nd digit are any of these:
{0,1,2,3,4,5}.  How many choices is that? _____

C. The ways to choose the 3rd digit are any of these:
{0,1,2,3,4,5}.  How many choices is that? _____

D. The ways to choose the 4th digit are any of these:
{0,1,2,3,4,5}.  How many choices is that? _____

E. Multiply the answers to questions A,B,C, and D together.
What do you get? _____

Now let's calculate how many we need to subtract from the answer
to question E.

We must not include any 4-digit numbers that start with 3 that
are even.  So let's see how many there are of those>

F. There is only one choice for the first digit of the numbers
we want to NOT include.  How many choices is that? <u>  1 </u> 
(I filled that in for you as 1 for it's the 1 digit "3"). 

G. The ways to choose the 2nd digit are any of these:
{0,1,2,3,4,5}.  How many choices is that? _____

H. The ways to choose the 3rd digit are any of these:
{0,1,2,3,4,5}.  How many choices is that? _____

I. But since the numbers we don't want to count are even, the
last (fourth) digit must be one of these (0, 2, 4).  How many
choices is that? _____

J. Multiply the answers for questions F,G,H, and I.  What do
you get? _____

K. Subtract the answer to J from the answer to E. What do you
get? _____

Should be 972.  If you don't get 972, tell me your answers to the
above questions in the thank-you note form below and I'll get back to
you by email.

Edwin</pre>