Question

The product of first $n$ odd natural numbers equals

• A. $\left({}^{2n}{C}_n\right)\left({}^n{P}_n\right)$
• B. ${\left(\frac{1}{2}\right)}^n\left({}^{2n}{C}_n\right)\left({}^n{P}_n\right)$
• C. ${\left(\frac{1}{4}\right)}^n\left({}^{2n}{C}_n\right)\left({}^{2n}{P}_n\right)$
• D. none of these

Answer 1

Answer: (B)

$\mathrm{1.3.5}\dots (2n-1)=\frac{(2n)!}{2^n(n!)}={\left(\frac{1}{2}\right)}^n\left({}^{2n}{C}_n\right)\left({}^n{P}_n\right)$