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 6?

Divisible by 6 means divisible by both 2 and 3. From Q102, divisible-by-3 numbers come from excluding 1 (digits {0,2,3,4}) or excluding 4 (digits {0,1,2,3}). For excluding 1 (digits {0,2,3,4}): need even last digit (0, 2, or 4). Last=0: 3!=6; Last=2: first from {3,4}, then 2!: 2×2=4; Last=4: first from {2,3}, then 2!: 2×2=4. Subtotal = 14. For excluding 4 (digits {0,1,2,3}): even last digit 0 or 2. Last=0: 3!=6; Last=2: first from {1,3}, 2×2=4. Subtotal = 10. Wait, recounting: total favorable = 14. Probability = 14/96 = 7/48.