1. ## number of ways

How many four digit numbers begin with an odd digit and end with an even one?

2. Originally Posted by pmullinax
How many four digit numbers begin with an odd digit and end with an even one?
Have you been taught the pigeon hole principle? Build in the restrictions and then re-arrange around them.

X X X X

In the first position there are 5 possibilities. In the last position there are 4 possibilities. Note that the number 0 is neither even nor odd.

Assumming repetition is allowed, there are 10 possibilities for the two positions in between.

Therefore: (5)(10)(10)(4) = 2000.

3. Hello, pmullinax!

How many four-digit numbers begin with an odd digit and end with an even one?

The first digit can be any odd digit: {1, 3, 5, 7, 9} . . . 5 choices.

The last digit can be any even digit: {0, 2, 4, 6, 8} . . . 5 choices.

The second and third digits can be any digit: 10² choices.

Therefore, there are: .5 × 5 × 10² .= .2500 such four-digit numbers.

4. ## great

I see why you are known as Mr. Fantastic!

Originally Posted by mr fantastic
Have you been taught the pigeon hole principle? Build in the restrictions and then re-arrange around them.

X X X X

In the first position there are 5 possibilities. In the last position there are 4 possibilities. Note that the number 0 is neither even nor odd.

Assumming repetition is allowed, there are 10 possibilities for the two positions in between.

Therefore: (5)(10)(10)(4) = 2000.