If an integer n is to be chosen at random from the integers 1 to 86, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8? Choose the correct choice from the following answers.
A) 1/4 B) 3/8 C) 1/2 D) 55/86 E) 3/4
n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.   Thus when n is even, this whole expression will be divisible by 8.   from 1 to 86, there are 43 even integers.   Now when (n+1) is multiple by 8, we have 12 such values for (n+1)   probability that n(n+1)(n+2) will be divisible by 8   = (43 + 12)/96   =55/86   Ans is55/86
<result>D</result>
If an integer n is to be chosen at random from the integers 1 to 86, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?