Multiple choice

Four cards are drawn at random from a pack of $52$ playing cards. The probability of getting all the four cards of the same suit is

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

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are 4 suits, each with 13 cards. The number of ways to choose 4 cards of the same suit is 4 * C(13, 4). The total ways to choose 4 cards from 52 is C(52, 4). Calculating this: 4 * (13*12*11*10 / 24) / (52*51*50*49 / 24) = 4 * 715 / 270725 = 2860 / 270725 = 44 / 4165.

AI explanation

The total number of ways to draw 4 cards from a pack of 52 is 52C4, which equals 270725. Since there are 4 suits and 13 cards in each suit, the number of ways to draw 4 cards of the same suit is 4 times 13C4, giving 4 times 715 = 2860. The probability is 2860 divided by 270725, which simplifies to 44/4165.

Keep practicing — related questions