Question

If ${}^{n}C_8={}^{n}C_2$. Find ${}^{n}C_2$.

Answer 1

Compute the required value

We know that if ${}^{n}C_a={}^{n}C_b\Rightarrow a=born=a+b$

${}^{n}C_8={}^{n}C_2\Rightarrow n=8+2=10$

$\therefore {}^{n}C_2={}^{10}C_2$

$$\begin{gathered} =\frac{10!}{2!(10-2)!} \\ =\frac{10!}{2!8!} \\ =\frac{10\times 9\times 8!}{2\times 1\times 8!} \\ =45 \end{gathered}$$

Hence, the value of ${}^{n}C_2$ is $45$.