Multiple choice

$A$ and $B$ draw two cards each, one after another, from a pack of well-shuffled pack of $52$ cards. The probability that all the four cards drawn are of the same suit is

  1. $\displaystyle \frac {44}{85 \times 49}$
  2. $\displaystyle \frac {11}{85 \times 49}$
  3. $\displaystyle \frac {13 \times 24}{17 \times 25 \times 49}$

  4. None of these
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A Correct answer
Explanation

Total ways to draw 4 cards = 52C4. Ways to draw 4 cards of same suit = 4 * 13C4. Probability = (4 * 13C4) / 52C4 = (4 * 13*12*11*10) / (52*51*50*49) = 44 / (17 * 5 * 49) = 44 / 4165. Simplifying 44 / (85 * 49) = 44 / 4165. Correct.

AI explanation

The total number of ways to draw 4 cards from 52 is 52C4, and the number of favorable ways is choosing 1 suit out of 4 and then drawing 4 cards from its 13 cards, which is 4 * 13C4. The probability is (4 * 13C4) / 52C4 = 44 / (4165). To match the format of the correct option, 4165 factors into 85 * 49. Therefore, the probability is 44 / (85 * 49).

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