In a​ lottery, the top cash prize was ​$673 ​million, going to three lucky winners. Players pick different numbers from 1 to 51 and one number from 1 to 43.
A player wins a minimum award of $150 by correctly matching numbers drawn from the white balls​ (1 through 51​) and matching the number on the gold ball​ (1 through 43​). What is the probability of winning the minimum​ award?