There are four aces, 12 face cards and 4 7s in a standard 52 card deck. The probability of getting an ace on the first draw is 4/52 or 1/13. For the second draw there are now 51 cards in the deck (assuming the draws are without replacement), so the probability of getting a face card is 12/51. Given an ace and a face card on the first two draws, the probability of a 7 on the third draw is 4/50 or 2/25. The probability of getting all three is 1/13*12/51*2/25.
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