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 2 ?

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 numbers = 4 24 = 96 . For the number to be divisible by 2 , the units digit must be 0, 2 , or 4 . Case 1: Units digit is 0 . The remaining 3 places can be filled in ⁴P₃ = 24 ways. Case 2: Units digit is 2 or 4 . The units place can be filled in 2 ways. The thousands place can be filled in 3 ways (excluding 0 and the un