Question

The number of ways of selecting 3 balls from a bag containing 5 red and 4 blue balls such that at least one is red is:

• A. 80
• B. 84
• C. 70
• D. 120

Hint:

"At least one" is almost always easiest to calculate using the complement method.

Answer 1

The Correct Option is A

Step 1: Concept
Total ways to select 3 balls - Ways to select 3 balls with NO red (all blue).
Step 2: Analysis
Total balls $= 5 + 4 = 9$. Total ways $= {}^{9}C_{3} = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} = 84$. Ways with only blue balls $= {}^{4}C_{3} = 4$.
Step 3: Conclusion
Ways with at least one red $= 84 - 4 = 80$.
Final Answer: (A)