20 Combination Problems

Please show all work.

Classify each problem according to whether it involves a permutation or a combination.
23. In how many ways can the letters of the word GLACIER be arranged?
24. A four-member committee is to be formed from a twelve-member board. In how many ways can it be formed?
27. In how many ways can nine different books be arranged on a shelf?
29. How many five-card poker hands can be dealt consisting of three queens and a pair?
30. In how many ways can a six-letter security password be formed from letters of the alphabet if no letter is repeated?

Solve the following problems.
34. In how many ways can five people line up at a checkpoint counter in a supermarket?
37. In how many ways can a member of a hiring committee select 3 of 12 job applicants for further consideration?
40. Find the number of distinguishable permutations that can be formed from the letters of the word PHILIPPINES.
42. In how many ways can five people boarding a bus be seated if the bus has eight vacant seats?
46. Book Selections. A student is given a reading list of ten books from which he must select two for an outside reading requirement. In how many ways can he make his selections?
52. Car Pools. A company car that has a seating capacity of six is used by six employees who have formed a car pool. If only four of these employees can drive, how many possible seating arrangements are there for the group?
53. Book Displays. At a college library, three mathematics books, four social science books, and three biology books are displayed on a shelf.
a. In how many ways can the ten books be arranged on the shelf?
b. In how many ways can the ten books be arranged on the shelf if books on the same subject are placed together?
54. Seating. In how many ways can four married couples attending a concert be seated in a row of eight seats if
a. There are no restrictions?
b. Each married couple is seated together?
c. The members of each sex are seated together?

62. Exams. A student taking an exam is required to answer exactly 10 out of 15 questions.
a. In how many ways can the 10 questions be selected?
b. In how many ways can the 10 questions be selected if exactly 2 of the first 3 questions must be answered?