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Q.

The product of first $n$ odd natural numbers equals

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a

none of these

b

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

c

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

d

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

answer is B.

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Detailed 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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