If C (n, 12) = C (n, 8), then C (22, n) is equal to
Question:

If C (n, 12) = C (n, 8), then C (22, n) is equal to

(a) 231

(b) 210

(c) 252

(d) 303

Solution:

(a) 231

${ }^{n} C_{12}={ }^{n} C_{8}$

$\Rightarrow n=12+8=20 \quad\left[\because{ }^{n} C_{x}={ }^{n} C_{y} \Rightarrow n=x+y\right.$ or $\left.x=y\right]$

Now, ${ }^{22} C_{n}={ }^{22} C_{20}$

$=\frac{22}{2} \times \frac{21}{1}$

$=231$

 

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