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I'm sure I'd get it wrong in real q though I'd think it is a bit suspicious to have a simple 1/2.
It's 5/8, or 60/96. From the net and simple calculation, we could get easy 48. However, we must notice that there are more numbers that are divisible by 8 under the term of (n)(n+1)(n+2). We have 12 more. For instance, 14x15x16, 15x16x17, 16x17x18...all three can be divided by 8.
probably would get this wrong in exam but.. all even numbers : n(n+1)(n+2) seem to be divisible by 8.(48 in all) all odd numbers, every odd number that is followed by a multiple of 8 will be divisble by 8, so we have 7,15,23,31,39,47,55,63,71,79,87,95. (12 in all) so probability = (48 + 12) / 96 = 60/96 = 5/8