If ^{2n}{C₂}{:^n}{C₂} = 9:2 and ^n{Cᵣ} = 10 , then r =

English

Gujarati

Hindi

6.Permutation and Combination

easy

If $^{2n}{C_2}{:^n}{C_2} = 9:2$ and $^n{C_r} = 10$, then $r = $

A

$1$

B

$2$

C

$4$

D

$5$

Solution

(b) $\left( {\frac{{(2n)\;!}}{{2\;!\;(2n – 2)\;!}}} \right)\,\,2 = \left( {\frac{{n\;!}}{{2\;!(n – 2)\;!}}} \right)\,\,9$

$ \Rightarrow (2n)(2n – 1)2 = 9n(n – 1) \Rightarrow n = 5$

Now $^5{C_r} = 10 \Rightarrow r = 2$.

Standard 11

Mathematics

Share

Similar Questions

How many numbers greater than $1000000$ can be formed by using the digits $1,2,0,2,4,2,4 ?$

medium

$^{n – 1}{C_r} = ({k^2} – 3)\,.{\,^n}{C_{r + 1}}$ if $k \in $

hard

(IIT-2004)

The number of arrangements of the letters of the word $SATAYPAUL$ such that no two $A$ are together and middle letter is consonant, is

normal

The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is

hard

(JEE MAIN-2020)

Determine $n$ if

$^{2 n} C_{3}:\,^{n} C_{3}=12: 1$

medium