1. CS336 F07 Counting 2

2. Example Consider integers in the set {1, 2, 3, …, 1000}. How many are divisible by either 4 or 10?

3. Example Given sets A and B, each of cardinality n>0, how many functions map A in a one-to-one fashion onto B?

4. Example Given the set of r symbols {a 1, …, a r }, how many different strings of length n>0 exist (allowing repetition)?

5. Example Given the set of r symbols {a 1, …, a r }, how many different strings of length n exist that contain exactly one a 1 (allowing repetition)?

6. Example Given the set of r symbols {a 1, …, a r }, how many different strings of length n exist that contain at least one a 1 (allowing repetition)?

7. Example Given the set of r symbols {a 1, …, a r }, how many different strings of length n exist that contain at least two a 1 ’s (allowing repetition)?

8. Example Given the set of r symbols {a 1, …, a r }, how many different strings of length n>0 exist (not allowing repetition)? Given the set of r symbols {a 1, …, a r }, how many different strings of length n exist that contain exactly one a 1 (not allowing repetition)? Given the set of r symbols {a 1, …, a r }, how many different strings of length n exist that contain at least one a 1 (not allowing repetition)?

9. Example Given the set of r symbols {a 1, …, a r }, how many different selections of length n>0 exist (ignoring order not allowing repetition)? Given the set of r symbols {a 1, …, a r }, how many different selections of length n exist that contain at least one a 1 (ignoring order and not allowing repetition)?

10. Example A be a set of cardinality p. Consider ordered strings of length m using the elements of A. How many such strings have the mth component a repetition of one of the preceding m-1?

11. Example For n>0, Let A = {1, 2, …, 2n}. How many subsets of A contain exactly k 1 even numbers and k 2 odd numbers?