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?

Hint: the product is divisible by $8$ if:


*

*One factor is divisible by 8, or

*One factor is divisible by 4 and another is divisible by 2, or

*All three factors are divisible by 2.


The last one is impossible in your situation (why?) What are the possible remainders when $n$ is divided by $8$ such that the first and second possibilities occur?
