Q1) Use a tree diagram to find the number of bit strings of length four with no three consecutive 0s.Draw the tree using / and \ for branches. And then say the total number of strings.

Q2) Show that if there are 30 students in a class, then at least two have last names that begin with the same letter.

Q3) How many numbers must be selected from the set {1, 3, 5, 7, 9, 11, 13, 15} to guarantee that at least one pair of these numbers add up to 16?

Q4) Suppose that there are nine students in a discrete mathematics class at a small college.Show that the class must have at least five male students or five female students.