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?

1. Assume you have ten (10) very expensive, leather bound books (all different authors) and you want to display these books on your fireplace mantle, but you are unsure how you want to arrange the books (by author, by height, year published, value . . . ). How many different ways can you arrange the books?
2. Assume you re

If you assume {v1, v2, ..., vk} and , and you also assume {v1, v2, ..., vk} are linearly independent and {v1, v2, ..., vk, w} are linearly dependent. How would you show that w can be uniquely expressed as a linear combination of {v1, v2, ..., vk}?
Also, if the zero vector is included among the vectors {v1, v2, ..., vk}, w

A typical "combination" lock is opened with the correct sequence of three numbers between 0 and 49 inclusive. (A number can be used more than once.) What is the probability of guessing those three numbers and opening the lock with the first try?

If T: U รข?' V is any linear transformation from U to V and B = {u 1, u 2, ..., u n} is a basis for U, then set T(B) = {T(u 1), T(u 2), ... T(u n)}
a. spans V
b. spans U
c. is a basis for V
d. is linearly independent
e. spans the range of T

Is one of the portfolio's expected return not in line with the fractor model relationship? Which one? Can you construct a combination of the other two portfolios that has the same factor sensitivity as the "out-of-line" portfolio? What is the expected return of that combination? What action would you expect investors to take wit

Can someone help me with this problem? I have attempted to answer Question A and would like for someone to tell me if I have answered it correctly. Part B of the question is asking for a graph and I can not get this to graph correctly. Part C and D is aking questions related to the graph. If someone can show me or assist me

I need help with these 6 problems
Section 8.1 #14
Section 8.2 #20,46
Section 8.3 #26
Section 8.4 #8,16
14. A menu offers a choice of 3 salads, 8 main dishes, and 5
desserts. How many different meals consisting of one
salad, one main dish, and one dessert are possible?
20. A group of 3 students is to be selected fro