Solve the following

Question:

If 20Cr + 1 = 20Cr − 1 , then r is equal to

(a) 10

(b) 11

(c) 19

(d) 12

Solution:

(a) 10

$r+1+r-1=20 \quad\left[\because{ }^{n} C_{x}={ }^{n} C_{y} \Rightarrow n=x+y\right.$ or $\left.x=y\right]$

$\Rightarrow 2 r=20$

 

$\Rightarrow r=10$

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