Basic Principles. How many different car license plates can be constructed if the licenses contain three letters followed by two digits (a) if repetitions are allowed. (b) if repetitions are not allowed. 8. Basic Principles. How many strings of length 5 formed using the letters ABCDEFG without repetitions (a) begin with AC or DB in that order? (b) contain letters B and D consecutively in either order (i.e., BD or DB)? 9. Basic Principles. A bit is a binary digit (a digit that is 0 or 1). How many eight-bit strings either start with a 1 or end with a 1 or both? 10. Permutations and Combinations. In how many ways can five distinct Martians and eight distinct Jovians wait in line if no two Martians stand together. 11. Permutations and Combinations. Let X = {a,b,c,d}. (a) Compute the number of 3-combinations of X. (b) List the 3-combinations of X. (c) Compute the number of 3-permutations of X. (d) List the 3-permutations of X.