Mega Millions is a multi-state lottery played in most U.S. states. As of this writing, the top cash prize was $656 million, going to three lucky winners in three states. Players pick five different numbers from 1 to 56 and one number from 1 to 46. Use this information to solve Exercises 27–30. Express all probabilities as fractions.

A player wins a minimum award of $150 by correctly matching three numbers drawn from white balls (1 through 56) and matching the number on the gold Mega Ball® (1 through 46). What is the probability of winning this consolation prize?