1. Find the number using the following Venn diagram. n(B) 2. Find the number using the following Venn diagram. n(A B) 3. Find the number using the following Venn diagram. n(Bc) 4. Find the number using the following Venn diagram. n(Ac B) 5. Given that n(A) = 20, n(B) = 12, n(A B) = 8, and n(U) = 40, fill in the four regions in the Venn diagram. 6. The sophomore lacrosse team has 26 players, of whom 10 played defense last year, 15 played offense, and 5 played both defense and offense, while the rest of the players did not play last year. How many members of the team played last year? = Players 7. A witness in a trial testified that he searched 21 cars, of which 12 were convertibles, 14 had outofstate plates, and 4 were convertibles with outofstate plates. Explain why the witness was not telling the truth. o The actual number of cars he searched was 22, which does not agree with the witness' testimony o that he searched 21 cars. The actual number of convertibles with outofstate plates would have to be 12, which does not agree with the witness' testimony that 4 convertibles had outofstate plates. o The actual number of cars he searched was 26, which does not agree with the witness' testimony o that he searched 21 cars. The actual number of convertibles would have to be 8, which does not agree with the witness' testimony that 12 cars were convertibles. 8. Calculate each factorial. (a) 2! (b) 3! 9. Calculate the quotient of factorials. 9 ! 7 ! 10. Determine the number of permutations. 9 P3 11. Find the number of combinations. 6C 3 12. A telephone number consists of seven digits, and the first digit cannot be a zero or a one. How many telephone numbers have no repeated digits? telephone numbers 13. You have 2 science books, 3 language books, and 5 philosophy books. In how many ways can they be arranged on the shelf if all books of the same subject are to be together? Ways