Multiple choice

In shuffling a pack of cards $3$ are accidently dropped, then the chance that missing card should be of different suits is

  1. $169/425$
  2. $261/425$
  3. $104/425$
  4. $425/169$
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A Correct answer
Explanation

Total ways to pick 3 cards is 52C3 = 22100. Ways to pick 3 cards of different suits is 4C3 * 13^3 = 4 * 2197 = 8788. Probability = 8788 / 22100 = 169 / 425.

AI explanation

Using combinations, the total number of ways to drop 3 cards from a 52-card deck is 52C3, equaling 22100. Since a standard deck has 4 suits of 13 cards each, the number of ways to drop one card from three different suits is 4C3 multiplied by 13C1 multiplied by 13C1 multiplied by 13C1, which equals 8788. The probability is 8788 / 22100, which simplifies to 2197 / 5525.

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