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What are the odds of choosing 7 or more face cards (jacks/queens/kings/aces) from 8 random playing cards? (self.math)

submitted 6 months ago by HonoraryMancunian to c/math

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I get about 1/1772 but I'm not confident

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[–] [email protected] 3 points 6 months ago (1 children)

((16 choose 7) * 36 + (16 choose 8)) / (52 choose 8)

Works out to about 1 chance in 1772, you are correct

[–] HonoraryMancunian 1 points 5 months ago (1 children)

I keep forgetting to ask, where did you get the 36 from?

[–] [email protected] 2 points 5 months ago

36 is the number of non face cards in the deck -- there are 16 face cards and 36 non face cards to choose from.

You might already know most of this, but just to break it down, the number of unordered selections of either 7 or 8 face cards is the sum of:

(16 choose 7), the number of selections of 7 face cards out of the 16 available
times 36, i.e. 52-16, the number of selections for the final, non-face card
then plus (16 choose 8), the number of selections of 8 face cards

So the first term gives us the number of hands that we're interested in, and then we divide it by the total number of hands possible (52 choose 8) to get probability.