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  4. If n C12= n C6, then n C2 is equal to

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Q. If ${ }^{n} C_{12}={ }^{n} C_{6}$, then ${ }^{n} C_{2}$ is equal to

BITSATBITSAT 2006

Solution:

Given ${ }^{n} C _{12}={ }^{n} C _{6}$
or ${ }^{n} C _{n-12}={ }^{n} C _{6}$
$\Rightarrow n -12=6$
$\Rightarrow n =18$
$\therefore n C _{2}={ }^{18} C _{2}=\frac{18 \times 17}{2 \times 1}$
$=153$