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I know what factorials are, obviously, and permutations and combinations, but what I Don't know is, given a problem with factorials in it, is there a general format for solving?

For instance, an old AMC 10 problem:

10B-#11. What is the tens digit in the sum 7! + 8! + 9! +

. . . + 2006! ?

(A) 1 (B) 3 (C) 4 (D) 6 (E) 9

How would one go about solving this?

All help appreciated!