Solve the following

Question:

If nC12 = nC6, then nC2 = ____________.

Solution:

Given nC12 = nC6

Using nCr = nCn

⇒ n − 6 = 12

 n = 18

$\Rightarrow^{18} C_{2}=\frac{18 \times 17 \times 16 !}{16 ! \times 2}$

$=9 \times 17$

i.e 18C = 153

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