1. How many bit strings of length 10 that neither start nor end with 007?

2. How many functions are there from the set {1, 2, 3, 4, 5} to the set {0, 1}?

3. Show that if 7 integers are selected from {1,2,...,10},there must be at least 2 pairs of these integers with the sum 11(for example 5 6=11)?

4. How many permutations of the letters ABCDEFGH contain the string BA?

5. Place these permutations of{1,2,3,4,5,6}in lexicographic order:234561,231456,165432,156423,543216?

6. Which is more likely: rolling a total of 8 when two dice are rolled or rolling a total of 8 when three dice are rolled?

7. Let R be the relation R = {(a, b)|a <b}on the set of integers. Find R−1 and R?

8. Which projection mapping is used to delete the second and the fourth components of a 6-tuple?

9. Let R be the relation on the set{1,2,3,4,5}containing the ordered pairs(1,2),(2,5),(3,4),(3,1),(4,2),(5,1),(5,3),and (5,4).Find R2?