The digits 2, 3, 4, 7, and 8 are each used once in a random order to form a five-digit number. what is the probability that the resulting number is divisible by 4? express your answer as a common fraction.

We have 5 digits. So there are: 5 * 4 * 3 * 2 * 1 = 120 five - digit numbers if we use each digit once. And : n = 120 ( all incomes )
If the resulting number is divisible by 4, then the last 2-digit number must be divisible by 4:  24, 28, 32, 48, 72, or 84 ( 6 in total ). And the first 3 digits of those numbers can be ordered in 3 * 2 * 1 = 6 ways.
m = 6 * 6 = 36 ( favorable incomes )
Probability = m / n = 36 / 120 = 3 / 10.
The probability is 3 / 10.