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## Homework Statement

----1. From the digits 0, 1, 2, 3, 4, 5, 6, how many four-digit numbers with distinct digits can be constructed? How many of these are even numbers?

----2. How many integers between 1000 and 9999 inclusive have distinct digits? Of these how many are odd numbers?

## Homework Equations

Use the product rule, etc.

## The Attempt at a Solution

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**1.**The first question is straight forward.

There are four-digit numbers: _ _ _ _

From left-to-right on possibilities: 6 (can't be zero; hence, 6 versus 7) * 6 * 5 * 4

Answer: 720 possibilities.

The second type of question is where the troubles begin.

Does anyone know of a simple online tutorial that would help? I'm sure this is all obvious but it is not to me.

The following is an attempt. . .

There are four-digit numbers: _ _ _ _

From right-to-left on possibilities: 3 (even numbers), 6 (even or odd), 5 (even or odd), 3 (even or odd but no zero)

Wrong answer: 270 possibilities.

Where am I going wrong?

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**2.**Again, the first part is easy for the second problem. The answer is 9*9*8*7 = 4,536.

The second part confuses me.

From right-to-left on possibilities: 5 (odd numbers), 9, 8, 6

Wrong answer: 5*9*8*6 = 2,160.

According to the textbook, from right-to-left the answer really is: 5, 8, 8, 7.

Why is this correct? Why those

*particular*numbers?