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combinatory

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Consider all possible permutations of eight distinct elements a, b, c, d, e, f, g, h. In how many of them, will d appear before b? Note that d and b may not necessarily be consecutive.
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These kinds of question can be solved by symmetry.

Total number of elements = 8

Total number of permutations = 8! = 40320

Half of these many orderings have d appear before b  and other half have b appear before d.

Thus answer = 8! / 2 = 20160
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