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This is more complex than it seems as you have to account for red fives and red face cards.

So it's the sum of the chances of drawing:

2/52 black 5, 20/51 red, 12/50 face

OR

2/52 red 5, 19/51 red, 12/50 face

OR

4/52 any 5, 6/51 red face, 11/50 face

(2/52)*(20/51)*(12/50) + (2/52)*(19/51)*(12/50) + (4/52)*(6/51)*(11/50) =

(480 + 456 + 264) / 132600 = 1200/132600 = 0.905%

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Q: If 3 cards are chosen from a standard deck what is the probability that you will pick a five a red card and a face card?
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