Q: On each of ten cards is one of the digits 0 to 9.
These numbers can be arranged in 10! ways.
How many of these 10 digit numbers are even?
How many of these 10 digit numbers are divisible by 3?

A: 1814400 even numbers, 3628800 are divisible by 3.

Half the numbers are even as each number will end with either an even or odd digit.
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800
10!/2 = 1814400

All of the 10 digit numbers are divisible by 3 as the digits add up to 45 and 45 is divisible by 3 (note; all th enumbers are also divisible by 9 because of the sum = 45).