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Suppose that n!!n!!n!! is defined as follows:
n!!={n×(n−2)×⋯×5×3×1if n is odd;n×(n−2)×⋯×6×4×2if n is even;1if n=0,−1. n!! = \begin{cases} n \times (n-2) \times \cdots \times 5 \times 3 \times 1 &\text{if } n \text{ is odd}; \\ n \times (n-2) \times \cdots \times 6 \times 4 \times 2 &\text{if } n \text{ is even}; \\ 1 &\text{if } n = 0, - 1. \\ \end{cases} n!!=⎩⎪⎨⎪⎧n×(n−2)×⋯×5×3×1n×(n−2)×⋯×6×4×21if n is odd;if n is even;if n=0,−1.
Then what is
9!6!!÷9!!6!?\color{#D61F06}{\dfrac{9!}{6!!}} \div \color{#20A900}{\dfrac{9!!}{6!}}?6!!9!÷6!9!!?
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