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 6 ?

Step-by-step solution

The total number of 4 -digit numbers that can be formed using the digits 0, 1, 2, 3, 4 without repetition is calculated by filling the thousands place in 4 ways (excluding 0 ) and the remaining 3 places in ⁴P₃ = 24 ways. Total numbers = 4 24 = 96 For a number to be divisible by 6 , it must be divisible by both 2 and 3 . For divisibility by 3 , the sum of the digits must be a multiple of 3 . The sum of all five digits is 0 + 1 + 2 + 3 + 4 = 10 . To choose 4 digits whose sum is a multiple of 3 , the excluded digit mu