If ^{2n}{C₃}:{,^n}{C₂} = 44:3 , then for which of following values of r , value of ^n{Cᵣ} will

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6.Permutation and Combination

easy

If $^{2n}{C_3}:{\,^n}{C_2} = 44:3$, then for which of the following values of $r$, the value of $^n{C_r}$ will be 15

A

$r = 3$

B

$r = 4$

C

$r = 6$

D

$r = 5$

Solution

(b) $\frac{{(2n)\;!}}{{(2n – 3)\;!\;.\;3\;!}} \times \frac{{2\;!\; \times (n – 2)\;!}}{{n\;!}}\; = \frac{{44}}{3}$

$ \Rightarrow 4(2n – 1) = 44$ $ \Rightarrow $ $2n = 12$ $ \Rightarrow $ $n = 6$

Now $^6{C_r} = 15$ $ \Rightarrow $$^6{C_r}{ = ^6}{C_2}$ or $^6{C_4}$ $ \Rightarrow $$r = 2,\;4$.

Standard 11

Mathematics

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(JEE MAIN-2023)