Question

If ${}^n{C}_3{:}^{n-1}{C}_4=8.5$ then the value of $n$ is

• A. $\frac{3}{2}$
• B. $8$
• C. $6$
• D. $12$

Answer 1

Answer: (B)

$8$

${}^n{C}_3{:}^{n-1}{C}_4=8:5$

$\frac{{}^n{C}_3}{{}^{n-1}{C}_4}=\frac{8}{5}$

$\frac{\frac{n!}{\left(n-3\right)!3!}}{\frac{\left(n-1\right)!}{\left(n-1-4\right)!4!}}=\frac{8}{5}$

$\frac{n}{(n-3)(n-4)}=\frac{2}{5}$

$5n=2(n^2-7n+12)$

$2n^2-19n+24=0$

$2n^2-16n-3n+24=0$

$(n-8)(2n-3)=0$

$n=8,\frac{3}{2}$

$n=8,(n\ne \frac{3}{2})$