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

  • @HonoraryMancunianOP
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    English
    124 days ago

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

    • mozz
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      fedilink
      224 days 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.