From a set containing $6$ positive and consecutive integers they are extracted, randomly and with replacement, three numbers $a, b, c$. Determine the probability that even $a^b + c$ generates as a result .
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2013 Shortlist LRP2 day1 (LRP = Logical Reasoning Probability)
Tags: probability, consecutive, number theory