Consider numbers of the form a = a₁a2a3 . . . an, with n digits, each digit from the set {1, 2, 3, 4, 5, 6, 7, 8}. For example, if n = 4, the number a = a₁ª2a3a4 will have 4 digits from the set {1, 2, 3, 4, 5, 6, 7, 8}. Let n = 7. a. How many such numbers are there? b. How many such numbers are there for which the sum of the digits is even? c. How many such numbers contain more even digits than odd digits?

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