Please answer all sections.

3. [12 points] How many strings are over the alphabet {a, b, c , d} have length 16 and satisfy the given additional restriction(s)? (a) No other restrictions. (b) The string starts with the character a. (c) The string has exactly six occurrences of the character c. (d) The string has at least one occurrence of the character b. (e) The string has the same number of occurrences of each character. (f) The last character in the string is either a or c