If ^m C_ 1 = ^n C_ 2 , is then : - Vidyadip

MCQ

If ${^\text{m}}\text{C}_{\text{1}}={^\text{n}}\text{C}_{\text{2}},$ is then :

A
$2m = n$
B
$2m = n(n + 1)$
✓
$2m = n(n - 1)$
D
$2n = m(m - 1)$

✓

Answer

Correct option: C.

$2m = n(n - 1)$

${^\text{m}}\text{C}_{\text{1}}={^\text{n}}\text{C}_{\text{2}}$
$\Rightarrow \frac{\text{m!}}{1!(\text{m}-1)!}$
$=\frac{\text{n!}}{2!(\text{n}-2)!}$
$\Rightarrow \frac{\text{m}(\text{m}-1)!}{(\text{m}-1)!}$
$=\frac{\text{n}(\text{n}-1)(\text{n}-2)!}{2!(\text{n}-2)!}$
$\Rightarrow2\text{m}=\text{n}(\text{n}-1)$

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