If ^ 10 C_r = ^ 10 C_ r + 2 , then ^5 C_r equals - Vidyadip

MCQ

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

A
$120$
B
$10$
C
$360$
✓
$5$

✓

Answer

Correct option: D.

$5$

d
(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$.

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