Question

If $C_{35}^{189}+C_X^{189}=C_X^{190}$, then $X$ is equal to

• A. $34$
• B. $35$
• C. $36$
• D. $37$

Answer 1

The correct option is C

$36$

Finding the value of $X$:

Given, $C_{35}^{189}+C_X^{189}=C_X^{190}$.

As We know,

${\mathit{C}}_{\mathbf{r}}^{\mathbf{n}}\mathbf{+}{\mathit{C}}_{\mathbf{r}\mathbf{-}\mathbf{1}}^{\mathbf{n}}\mathbf{=}{\mathit{C}}_{\mathbf{r}}^{\mathbf{n}\mathbf{+}\mathbf{1}}$

$\Rightarrow$ $n=189$

$\Rightarrow$ $n+1=190$

Also,

$r=X$

$\Rightarrow$ $r-1=35$

$\Rightarrow$$X-1=35$

$\Rightarrow$ $X=36$

Hence, Option (C) is the correct answer.