Multiple choice

In a box, there are $8$ alphabets cards with the letters: $S, S, A, A, A, H, H, H$. Find the probability that the word $ASH$ will form if three cards are drawn simultaneously.

  1. $\dfrac{9}{28}$
  2. $\dfrac{19}{28}$
  3. $\dfrac{9}{14}$
  4. $\dfrac{5}{14}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total ways to choose 3 cards from 8 is C(8,3) = 56. To get 'ASH', we need one A (from 3), one S (from 2), and one H (from 3). Ways = 3 * 2 * 3 = 18. Probability = 18/56 = 9/28.

AI explanation

The total number of ways to draw 3 cards simultaneously from 8 is 8C3, which equals 56. To form the word ASH, we must draw one A from 3, one S from 2, and one H from 3, giving 3C1 times 2C1 times 3C1, which equals 18. Dividing the favorable outcomes by the total outcomes gives 18/56, which simplifies to 9/28. The result is 9/28.