If = ^m C_2 , then ^C_2is equal to - Vidyadip

MCQ

If $\alpha { = ^m}{C_2}$, then $^\alpha {C_2}$is equal to

A
$^{m + 1}{C_4}$
B
$^{m - 1}{C_4}$
C
$3\,.{\;^{m + 2}}{C_4}$
✓
$3\;.{\;^{m + 1}}{C_4}$

✓

Answer

Correct option: D.

$3\;.{\;^{m + 1}}{C_4}$

d
(d) $\alpha { = ^m}{C_2} \Rightarrow \alpha = \frac{{m(m - 1)}}{2}$

$\therefore $$^\alpha {C_2}{ = ^{m(m - 1)/2}}{C_2} = \frac{1}{2}.\frac{{m(m - 1)}}{2}\left\{ {\frac{{m(m - 1)}}{2} - 1} \right\}$

$ = \frac{1}{8}m(m - 1)(m - 2)(m + 1)$

$ = \frac{1}{8}(m + 1)\;m(m - 1)(m - 2) = 3\;.{\;^{m + 1}}{C_4}$

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