Set over Set Problem

[bighomage]

Pretty basic but I'm not sure I know how to do the math. I think I do, but I wanted to make sure I'm not wrong. AA vs. 77 in Texas Hold Em. The first community card dealt is a 7. What are the odds that an ace will hit on one of the next four cards?

[jordanx]

AA vs 77

7 x x x x

47 unseen cards, 2 aces left

2/47 + 2/46 + 2/45 + 2/44 = .176 or around 18% chance.

[LetYouDown]

1 - C(45,4)/C(47,4) = 16.5% or about 5-to-1. Note: This includes boards that have the case 7 and both aces.

[LINES]

is that also a right way to do it? Becuase, i don't exactly understand the Choose function and how it applies to 52 cards, or 47 cards remaning.

EDIT: Referring to jordans way