1. Tardigrade
  2. Question
  3. Mathematics
  4. 2 n C3: n C2=44: 3 then value of n C3 is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. ${ }^{2 n} C_3:{ }^n C_2=44: 3$ then value of ${ }^n C_3$ is

Binomial Theorem

Solution:

$\frac{{ }^{2 n} C _3}{{ }^{ n } C _2}=\frac{44}{3} \Rightarrow 3 \cdot{ }^{2 n} C _3=44 \cdot{ }^2 C _2$
$ \Rightarrow 3 \cdot \frac{2 n (2 n -1)(2 n-2)}{3 !}=44 \cdot \frac{ n ( n -1)}{2 !}$
$\Rightarrow 4 n(n-1)(2 n-1)-44 n(n-1)=0 $
$ \Rightarrow 4 n(n-1)(2 n-1-11)=0$
$\Rightarrow n=6$