If ^{10}{Cᵣ}{ = ^{10}}{C_{r + 2}} , then ^5{Cᵣ} equals

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6.Permutation and Combination

easy

If $^{10}{C_r}{ = ^{10}}{C_{r + 2}}$, then $^5{C_r}$ equals

A

$120$

B

$10$

C

$360$

D

$5$

Solution

(d) $^{10}{C_r}{ = ^{10}}{C_{r + 2}}$

$\Rightarrow r + r + 2 = 10 $

$\Rightarrow r = 4$

$\therefore $$^5{C_r}{ = ^5}{C_4} = \frac{{5\;!}}{{1\;!\;4\;!}} = 5$.

Standard 11

Mathematics

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