Solve the following

Question:

If 15C3r = 15Cr + 3 , then r is equal to

(a) 5

(b) 4

(c) 3

(d) 2

Solution:

(c) 3

$3 r+r+3=15 \quad\left[\because{ }^{n} C_{x}={ }^{n} C_{y} \Rightarrow n=x+y\right.$ or $\left.x=y\right]$

$\Rightarrow 4 r+3=15$

$\Rightarrow 4 r=12$

$\Rightarrow r=3$

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