Question

A box contains 5 red and 4 blue balls. In how many ways can 4 balls be chosen such that there are at most 3 balls of each colour?

• A. 132
• B. 242
• C. 60
• D. 120
• E. 240

Hint:

“At most” → exclude extremes, split into valid distribution cases.

Answer 1

The Correct Option is D

Step 1: Restriction.
Exclude 4R and 4B cases.
Step 2: Valid cases.
- 3R+1B: \(\binom{5}{3}\binom{4}{1}=40\).
- 2R+2B: \(\binom{5}{2}\binom{4}{2}=60\).
- 1R+3B: \(\binom{5}{1}\binom{4}{3}=20\).

Step 3: Add.
Total = \(40+60+20=120\).
Final Answer:
\[ \boxed{120} \]