Question about combinatorics

Question

1. How many ways to arrange numbers 2,5,6,0,1 to get an odd three digit number where all digits are different?
2. How many ways there are to construct a five digit number, divisible by 2, with all different digits.
3. The number is composed of 6 digits, the first one is always 5. How many ways there are to compose the number with different digits?

Answer 1

1. We have to work from the end. We only have 1 and 5 to choose from as final digits, so two choices.

As for the 2nd digit, we can use any of the other four. Once we use two of the digits, we can pick any of the remaining three for the first digit.

2 x 4 x 3 = 24 ways.

2. To be divisible by 2, our number has to be even. We have 0,2,4,6,and 8 as choices, so five choices.

There are a total of ten signgle digits, 0-9. After using one, we are left with 9, and so on.

5 x 9 x 8 x 7 x 6 = your answer

3. Now we start from the beginning. I bet you can get this one!