Question

The product of first $n$ odd natural numbers equals

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

Answer 1

Answer: (B)

$1.3 .5 \ldots(2 n-1)=\frac{(2 n) !}{2^n(n !)}=\left(\frac{1}{2}\right)^n\left({ }^{2 n} C_n\right)\left({ }^n P_n\right)$