We can also look for a pattern for such questions!

Let, x = n(n +1)(n+2)

When n=1, x is not divisible by 8
When n=2, x is divisible by 8
When n=3, x is not divisible by 8
When n=4, x is divisible by 8
When n=5, x is not divisible by 8
When n=6, x is divisible by 8
When n=7, x is divisible by 8
When n=8, x is divisible by 8
And the pattern would continue ...

We can notice that for 5 integers out of every 8 are divisible by 8. And since the total number of integers are divisible by 8. The Prob. would stay 5/8.

Option D