Interview Question: Winning Big

Sample Question #312 (probability theory)
 
Consider the following two lottery games:
 
Game 1:  you pick 5 unique numbers from 1 to 52. You win the jackpot if all five numbers of yours match the winning numbers.
 
Game 2:  you pick 3 unique numbers from 1 to 20. You win the jackpot if all three numbers of yours match the winning numbers.
 
Two questions for you: (1) Calculate the probability of winning the jackpot in each game; (2) Calculate the probability of winning both games. Of couse, we assume you play each game once.
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