Multiple choice

Four cards are drawn at a time from a pack of $52$ playing cards. Find the probability of getting all the $4$ cards of the same suit.

  1. $\cfrac{44}{4165}$
  2. $\cfrac{11}{4165}$
  3. $\cfrac{22}{4165}$

  4. none of these
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A Correct answer
Explanation

Total ways to choose 4 cards = C(52, 4) = 270725. Ways to choose 4 cards of one suit = 4 * C(13, 4) = 4 * 715 = 2860. Probability = 2860 / 270725 = 44 / 4165.

AI explanation

The total number of ways to draw 4 cards from a pack of 52 is given by the combination formula 52C4, which equals 270725. Since there are 4 suits with 13 cards each, the number of ways to draw 4 cards of the same suit is 4 multiplied by 13C4, giving 4 * 715 = 2860. The probability is 2860 / 270725, which simplifies by dividing the numerator and denominator by 65 to yield 44/4165.

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