How many bit strings of length eight either begin with two 0's or end with three I's? The name of a variable in the C programming language is a string that can contain uppercase letters, lowercase letters, digits, or underscores. Further, the first character in the string must be a letter, either uppercase or lowercase, or an underscore. If the name of a variable is determined by its first five characters, how many different variables can be named in C? (Note that the name of a variable may contain fewer than five characters.) A bowl contains 10 red balls and 10 blue balls. A woman selects balls at random without looking at them, a) How many balls must she select to be sure of having at least 4 balls of the same color? b) How many balls must she select to be sure of having at least 4 blue balls? There are 8 computers. Each computer is directly connected to at least one of the other computers. Show that there are at least two computers in that are directly connected to the same number of other computers. How many bit strings of length 12 contain exactly three 1s? at most three 1s? at least three 1s? an equal number of Os and 1s? How many permutations of the letters ABCDEFGHU contain the string JH? the strings AC, DE. and JH? the strings CAB and BED? the strings BCA and ABF? How many ways are there for 8 women and 5 men to stand in a line so that no two men stand next to each other? How many ways arc there to distribute 10 indistinguishable balls into 5 distinguishable bins? Every day a student randomly chooses a sandwich for lunch from a pile of wrapped sandwiches. If there are six kinds of sandwiches, how many different ways are there for the student to choose sandwiches for the seven days of a week if the order in which the sandwiches arc chosen matters? A shelf holds 12 books in a row. How many ways arc there to choose five books so that no two adjacent books are chosen