Question
A 6-digit number is formed using the digits 1, 2, 3, 4, 5 and 6. If each digit can be used only once, then find the probability that the number formed will be divisible by 4.
Solution
Total numbers formed = 6! = 720
For divisibility by 4, the last two digits of the number must form a number divisible by 4
From digits 1–6, valid 2-digit endings divisible by 4 without repetition are: 12, 16, 24, 32, 36, 52, 56, 64 → total = 8 combinations
For each, remaining 4 digits can be arranged in 4! = 24 ways
Total such numbers = 8 × 24 = 192
Required probability = 192/720 = 4/15
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