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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