1. Find the number using the following Venn diagram. n(U) 2. Find the number using the following Venn diagram. n(A B) 3. Find the number using the following Venn diagram. n(Ac) 4. Given that n(A) = 20, n(B) = 10, n(A B) = 6, and n(U) = 38, fill in the four regions in the Venn diagram. 5. How many six-symbol computer passwords can be formed using the letters A to J and the digits 3 to 7? Passwords 6. Calculate the quotient of factorials. 8! 5! 7. Determine the number of permutations. 6 P3 8. Find the number of combinations. 8 C2 9. A computer password is to consist of five alphanumeric characters with no repeats. (An alphanumeric character is a letter from A to Z or a digit from 0 to 9.) How many such passwords are there? passwords How many are there if the letter O and the digit 0 are excluded to avoid confusion? passwords 10. A junior high girls' basketball team is to consist of 5 players. How many different teams can the manager select from a roster of 9 girls? Teams 11. If a committee of 3 is to be chosen at random from a class of 13 students, what is the probability of any particular committee being selected? (Enter your answer as a fraction.) What if the committee is to consist of a president, a vice president, and a treasurer? (Enter your answer as a fraction.)