COMEDK2024Evening ShiftMathematicsProbabilityActual
While shuffling a pack of cards, 3 cards were accidently dropped, then find the probability that the missing cards belong to different suits?
Options
- A261 425
- B104 425
- C169 261
- 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