AMC 12 2019a Problem 3

A box contains $28$ red balls, $20$ green balls, $19$ yellow balls, $13$ blue balls, $11$ white balls, and $9$ black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least $15$ balls of a single color will be drawn?

$\textbf{(A) } 75 \textbf{(B) } 76 \textbf{(C) } 79 \textbf{(D) } 84 \textbf{(E) } 91$