Hint.You can use the concepts from Set theory and Set operations (Union, Intersection,Set Difference etc.) to solve the counting problems.

2. [4 pts) How many strings of six lowercase letters from the English alphabet contain (a) the letter a, if letters can be repeated? (b) the letters a and b, if letters can be repeated? (c) the letters a and b in consecutive positions with a preceding b, with all the letters distinct? (d) the letters a and b, where a is somewhere to the left of b in the string, with all the letters distinct