If α { = ^m}{C₂} , then ^α {C₂} is equal to

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6.Permutation and Combination

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

A

$^{m + 1}{C_4}$

B

$^{m - 1}{C_4}$

C

$3\,.{\;^{m + 2}}{C_4}$

D

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

Solution

(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}$

Standard 11

Mathematics

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