First slide

Permutations

Question

The product of first $n$ odd natural numbers equals

Moderate

A

$(^{2 n} C_{n}) (^{n} P_{n})$
B

${(\frac{1}{2})}^{n} (^{2 n} C_{n}) (^{n} P_{n})$
C

${(\frac{1}{4})}^{n} (^{2 n} C_{n}) (^{2 n} P_{n})$
D

none of these

Solution

$1.3.5 \dots (2 n - 1) = \frac{(2 n)!}{2^{n} (n!)} = {(\frac{1}{2})}^{n} (^{2 n} C_{n}) (^{n} P_{n})$

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