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 2.
Solution
Total numbers formed = 6! = 720
To be divisible by 2, the unit digit must be even → 2, 4 or 6
Fix unit digit as 2 → remaining 5 digits can be arranged in 5! = 120 ways
Same for unit digit 4 → 5! = 120
Same for 6 → 5! = 120
Total such numbers = 3 × 120 = 360
Required probability = 360/720 = 1/2
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