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COMEDK20269 May 2026Evening ShiftMathematicsProbabilityActual

Cards are numbered from 12 to 51. Two cards are drawn one after the other without replacement. Find the probability that one card is a multiple of 6 and the other card is a multiple of 8 .

Options

  1. A4 65
  2. B3 52
  3. C7 156
  4. D8 195

Correct answer

D. 8 195

Step-by-step solution

Total number of cards is 51 - 12 + 1 = 40 . Let A be the set of cards which are multiples of 6 and B be the set of cards which are multiples of 8 . A = 12, 18, 24, 30, 36, 42, 48 n(A) = 7 B = 16, 24, 32, 40, 48 n(B) = 5 A B = 24, 48 n(A B) = 2 Since two cards are drawn one after the other without replacement, the total number of ordered draws is 40 39 = 1560 . Let E₁ be the event that the first card is in A and the second is in B . The number of such draws is n(A) n(B) minus the cases where the same card is drawn t

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