Solve the following

Question:

If 43Cr − 6 = 43C3r + 1 , then the value of r is

(a) 12

(b) 8

(c) 6

(d) 10

(e) 14

Solution:

(a) 12

$r-6+3 r+1=43 \quad\left[\because{ }^{n} C_{x}={ }^{n} C_{y} \Rightarrow n=x+y\right.$ or $\left.x=y\right]$

$\Rightarrow 4 r-5=43$

$\Rightarrow 4 r=48$

$\Rightarrow r=12$

 

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