What is the probability that the number selected is divisible by 3 ?
For the next five (05) items that follow : 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).
- A. \frac{9}{28}
- B. \frac{3}{8} ✓
- C. \frac{1}{4}
- D. \frac{5}{16}
Correct Answer: B. \frac{3}{8}
Explanation
For divisibility by 3, the sum of digits must be a multiple of 3. The sum of all 5 given digits is 10. To get a 4-digit sum divisible by 3, we must leave out either 1 (sum=9) or 4 (sum=6). Without 1: {0,2,3,4} forms 3*3*2*1=18 numbers. Without 4: {0,1,2,3} forms 3*3*2*1=18 numbers. Total = 36. Probability = 36/96 = 3/8.
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