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While shuffling a pack of cards, 3 cards were accidently dropped, then find the probability that the missing cards belong to different suits?

Options

  1. A261 425
  2. B104 425
  3. C169 261
  4. D169 425

Correct answer

D. 169 425

Step-by-step solution

The total number of ways to choose 3 cards from a pack of 52 cards is ⁵²C₃ = 52 51 50 3 2 1 = 22100 . The number of ways to choose 3 cards such that they belong to different suits is calculated by first choosing 3 suits out of 4, which can be done in ⁴C₃ = 4 ways. Then, from each of the 3 chosen suits, we choose 1 card out of 13, which can be done in ¹³C₁ ¹³C₁ ¹³C₁ = 13³ = 2197 ways. The total number of favorable outcomes is 4 2197 = 8788 . The probability is 8788 22100 . Dividing both numerator and denominator by

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