Question

If ${}^n$C${}_2$ + ${}^n$C${}_3$ = ${}^6$C${}_3$ and ${}^n$C${}_x$ = ${}^n$C${}_3$, x ≠ 3, then the value of x is equal to

• A. 5
• B. 4
• C. 2
• D. 6
• E. 1

Answer 1

Answer: (C)

Given, ${}^n{C}_2+{}^n{C}_3={}^6{C}_3$
$\Rightarrow n=5\left[\because {}^n{C}_r+{}^n{C}_{r-1}={}^{n+1}{C}_r\right]$
and ${}^n{C}_x={}^n{C}_3\Rightarrow {}^5{C}_x={}^5{C}_3$
$\Rightarrow x=5-3=2$
$[\because$ If ${}^n{C}_{r1}={}^n{C}_{12}\Rightarrow$ either $r_1=r_2$ or $n=r_1+r_2]$