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

Rationale: "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 isd"
Answer: D