I roll three fair six-sided dice (with faces 1, 2, 3, 4, 5, 6) and arrange the results to form a three-digit number.

For example, if I rolled 2, 3 and 5, I could make the numbers 253, 523, etc.

What is the probability that I can arrange the dice to make a number that is...

a) divisible by 2?

b) divisible by 3?

c) divisible by 6?

d) divisible by 9?