Solve the following
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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