Passage: 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). Question: What is the probability that the number selected is divisible by 3 ?

Step-by-step solution

Total number of 4 -digit numbers formed using 0, 1, 2, 3, 4 without repetition: The thousands place can be filled in 4 ways (excluding 0 ). The remaining 3 places can be filled in ⁴P₃ = 24 ways. Total possible numbers = 4 24 = 96 . A number is divisible by 3 if the sum of its digits is a multiple of 3 . The sum of all given digits is 0 + 1 + 2 + 3 + 4 = 10 . To choose 4 digits whose sum is a multiple of 3 , the excluded digit must leave a remainder of 1 when divided by 3 . Thus, the excluded digit can be 1 or 4 . C