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Darrell has a collection of 40 DVDs, each of which contains one movie. There are 17 comedy movies, 14 fantasy movies, and 9 historical movies, where each historical movie takes place in a separate time period. The movies will be ordered on a shelf from left to right so that the movies of each type comedy, fantasy and historical are in a single group of consecutive movies. In addition, the historical movies will be ordered from earliest time period to latest time period. How many possible orderings of the movies are there?

A.(17!)(14!)(3!)
B.(17!)(14!)(9!)
C.(17!)(14!)(9!)(3!)
D.$$\frac{(40!)}{(17!)(14!)(9!)}$$
E.$$\frac{(40!)(3!)}{(17!)(14!)}$$

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6.3.8 其他特殊排列组合技巧

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