19. In how many ways can the 12 members of the glee club line up for a club picture?

33. In how many ways can the 9-person batting order of a baseball team be made up, assuming the pitcher bats last?

39. A fair coin is flipped 8 times and the sequence of heads and tails is noted. In how many outcomes are there A. exactly 6 heads? B. at least 3 heads? C. at most 6 heads? D. at most 2 heads?

41. In how many ways can 4 different contracts be awarded to 7 different firms, assuming that no firm can be awarded more than one contract?

45. A company has 15 male employees and 17 female employees. The CEO wants to invite a group of employees to join her for lunch. Each employee is equally likely to be chosen. In how many ways can a group of 8 employees be selected if the group contains A. 3 women and 5 men?

B. at most 2 women?

C. at least 6 women?

D. at least 1 woman?

53. Suppose that you want to rearrange your textbooks on a bookshelf so that they are arranged by subject. You have 4 history books, 3 science books and 8 literature books. In how many ways can you arrange the books? Assume that all books are different.

55. Suppose that 5 couples go to the movies together. In how many ways can the seating be arranged if A. there are no restrictions on the seating?

B. each couple must sit together?

57. Suppose that a band called the Wonders is going on tour. They currently have 7 locations confirmed, 4 in Texas and 1 each in Louisiana, Arkansas and Oklahoma. They now want to set the dates for the concerts. How many possible itineraries does the band have if A. there are no restrictions?

B. they must play all of the Texas concerts in succession?

59. The by-laws of an organization require that all votes be passed by a majority of the membership that is in attendance at the vote and also by a unanimous vote of the 4 member executive committee. Suppose that there are 11 members present at a vote, including all 4 members of the executive committee. In how many ways can a motion be passed?