# Treble Trouble!

**Discrete Mathematics**Level 4

\[ \large 2^a + 2^b + 2^c \]

We are given the natural numbers \(1\leq a \leq 100\), \(1\leq b \leq 50\), \(1 \leq c \leq 25 \). If the total possible number of ordered triplets \((a,b,c) \) such that the expression above is divisible by \(3\) is \(k\), evaluate \(k\).