Question:
If n + 1C3 = 2 · nC2 , then n =
(a) 3
(b) 4
(c) 5
(d) 6
Solution:
(c) 5
${ }^{n+1} C_{3}=2 \times{ }^{n} C_{2}$
$\Rightarrow \frac{(n+1) !}{3 !(n-2) !}=2 \times \frac{n !}{2 !(n-2) !}$
$\Rightarrow \frac{(n+1) n !}{3 \times 2 !(n-2) !}=2 \times \frac{n !}{2 !(n-2) !}$
$\Rightarrow n+1=6$
$\Rightarrow n=5$
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