In the expansion of (1+x)^{p}(1+x)^{q}, if the coefficient of x^{3} is 35, then what is the value of (p+q)?
- A. 5
- B. 6
- C. 7 ✓
- D. 8
Correct Answer: C. 7
Explanation
The expression simplifies to (1+x)^{p+q}. The coefficient of x^3 in this expansion is \binom{p+q}{3}. Setting \binom{n}{3} = 35 gives n(n-1)(n-2) = 210, which implies n = p+q = 7.
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