Question

A bag contains 7 white and 8 red balls. If 10 balls are drawn at random from the bag, what is the probability that 6 balls are white and the rest are red?

• A. 1/4
• B. 70/429
• C. 3/5
• D. 35/143

Hint:

When drawing items without replacement, always use combinations, not permutations, since order does not matter.

Answer 1

The Correct Option is D

Step 1: Total possible ways to draw 10 balls.
Total balls = 15. Ways of drawing 10 = \( \binom{15}{10} \).
Step 2: Favourable ways.
Choose 6 white from 7: \( \binom{7}{6} \). Choose 4 red from 8: \( \binom{8}{4} \).
Thus favourable = \( \binom{7}{6} \times \binom{8}{4} = 7 \times 70 = 490. \)
Step 3: Probability.
Total = \( \binom{15}{10} = 3003 \).
Probability = \( \frac{490}{3003} = \frac{35}{143}. \)
Step 4: Conclusion.
Thus the required probability is 35/143.