Probability that an integer is divisible by $8$ If $n$ is an integer from $1$ to $96$ (inclusive), what is the probability that $n(n+1)(n+2)$ is divisible by 8?

If n is from
1 to 96,
it is divisible by 8
if it is of the form
8m+k
where
k = 0, 2, 4, 6, or 7.
There are
5(96/8) = 60
from 1 to 96.
Therefore the probability is
60/96 = 5/8.
