16 players \( \mathrm{P}_{1}, \mathrm{P}_{2}, \mathrm{P}_{3}, \ldots \ldots . . \mathrm{P}_{16} \) take part in a tennis tournament. Lower suffix player is better than any higher suffix player. These players are to be divided into 4 groups each comprising of 4 players and the best from each group is selected for semifinals.
Number of ways in which 16 players can be divided into four equal groups, is
(A) \( \frac{35}{27} \prod_{r=1}^{8}(2 r-1) \)
(B) \( \frac{35}{24} \prod_{r=1}^{8}(2 r-1) \)
(C) \( \frac{35}{52} \prod_{\mathrm{r}=1}^{8}(2 \mathrm{r}-1) \)
(D) \( \frac{35}{6} \prod_{\mathrm{r}=1}^{8}(2 \mathrm{r}-1) \)
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