If C(n, 12) = C(n, 8) is then r equal to: - Vidyadip

MCQ

If $C(n, 12) = C(n, 8)$ is then $r$ equal to:

✓
$231$
B
$210$
C
$252$
D
$303$

✓

Answer

Correct option: A.

$231$

${^\text{n}}\text{C}_{\text{12}}={^\text{n}}\text{C}_{\text{8}}$
$\Rightarrow \text{n}=12+8=20$
${^\text{n}}\text{C}_{\text{x}}={^\text{n}}\text{C}_{\text{y}}$
$\Rightarrow \text{n}=\text{x}+\text{y}, \text{x}=\text{y}$
Now,
${^\text{22}}\text{C}_{\text{n}}={^\text{22}}\text{C}_{\text{20}}$
$=\frac{22}{2}\times\frac{21}{1}$
$=231$

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