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Odds Of Four Aces?

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What are the chances of all 4 aces being at the top of stacks at the start of a game of Klondike / Patience solitaire? The answer is simple!

Was I lucky, or is this an edited image because I'm not lucky? You be the judge!

The odds are 1/7,735 (or 7,735:1) for all four aces to be shown face up in the layout.

I am not a mathematician.

( 4 / 52 ) * ( 3 / 51 ) * ( 2 / 50 ) * ( 1 / 49 ) * 35 = ~0.0129% chance of seeing all four aces, or a ~99.9871% chance of not seeing all four aces as starting face up cards.

Written another way it's (7 nCr 4) / (52 nCr 4).

If you want a better explanation ask your math teacher!

Good luck! 😇


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