A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed). What is the probability that the number selected is divisible by 4?

For divisibility by 4, last two digits must form a number divisible by 4. Possible last-two from {0,1,2,3,4}: 04, 12, 20, 24, 32, 40. For each, count valid arrangements of first two digits (first ≠ 0). Last two = 04: first two from {1,2,3}, arrangements 3×2 = 6. Last two = 12: from {0,3,4}, first ≠ 0, so 2×2 = 4. Last two = 20: from {1,3,4}, 3×2 = 6. Last two = 24: from {0,1,3}, 2×2 = 4. Last two = 32: from {0,1,4}, 2×2 = 4. Last two = 40: from {1,2,3}, 3×2 = 6. Total = 6+4+6+4+4+6 = 30. Probability = 30/96 = 5/16.