3. (40 points, 8+2 points each) Give a regular expression for the following languages (8 points). Explain the expression by writing what each part does (2 points). (a) The set of strings over {a,b,c} that contains at least one a and ends in bb. (b) The set of strings over {a,b,c} that have a number of a's, followed by a number of b's, and followed by a number of c's. (The number of a's, b's, and c's can be different.) It is possible that there are no a's, or bs, or c's and the string is empty. (c) The set of strings over {a,b,c} that have a number of a's, followed by a number of bs, and followed by a number of c's. (The number of a's, b's, and c's can be different.) It is possible that there are no a's, or b's, or c's, but is not in the language. (d) The set of strings over {1, 2, 3, a} that do not begin with 123