Multiple choice

The face cards are removed from a full pack. Out of the remaining $40$ cards, $4$ are drawn at random. What is the probability that they belong to different suits?

  1. $\dfrac {1000}{9139}$
  2. $\dfrac {1001}{9136}$
  3. $\dfrac {100}{913}$
  4. $\dfrac {1002}{9129}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total cards = 40. Choosing 4 cards = 40C4 = 91390. Choosing one from each suit = 10C1 * 10C1 * 10C1 * 10C1 = 10000. Probability = 10000 / 91390 = 1000 / 9139.

AI explanation

The total number of ways to draw 4 cards from 40 is calculated using the combinations formula as 40 C 4, which equals 91390. Since there are 10 cards in each suit, the number of ways to draw one card from each of the four suits is 10 C 1 multiplied by itself four times, or 10^4, which equals 10000. The probability is therefore 10000 / 91390, which simplifies to 1000 / 9139.

Keep practicing — related questions