A lottery winner from State $F$ must match, in any order, $6$ balls randomly chosen from a single pool of balls

A lottery winner from State $F$ must match, in any order, $6$ balls randomly chosen from a single pool of balls numbered from $1$ to $50.$ A lottery winner from State $G$ must match, in any order, $5$ balls randomly chosen from a first pool of balls numbered from $1$ to $50$ AND a “megaball,” randomly chosen from a second set of balls numbered from $1$ to $50.$ The number of winning combinations in a single drawing of the lottery in State $G$ is what percentage greater than the number of winning combinations in a single drawing of the lottery in State $F?$

A. $11\%$
B. $85\%$
C. $111\%$
D. $567\%$
E. $667\%$

OA D

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