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 4 ?

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 4 if the number formed by its last two digits is divisible by 4 . The possible last two digits from the given set are 04, 12, 20, 24, 32, 40 . Case 1: Last two digits are 04, 20 , or 40 ( 3 cases). Since 0 is used, the first two places can be filled from the rema