Count the number of strings of length 9 over the alphabet {a, b, c} subject to each of the following restrictions.

(a)

The first or the last character is a.

(b)

The string contains at least 8 consecutive a's.

(c)

The string contains at least 8 consecutive identical characters.

(d)

The first character is the same as the last character, or the last character is a, or the first character is a.

(e)

The string contains at least seven consecutive a's.

(f)

The characters in the string "abababa" appear consecutively somewhere in the 9-character string. (So "ccabababa" would be such a 9-character string, but "cababcaba" would not.)

(g)

The string has exactly 2 a's or exactly 3 b's.

(h)

The string has exactly 2 a's or exactly 2 b's or exactly 2 c's