Chapter 6 Practice Test 2008

Chapter 6 Practice Test 2008 Name ______

1. The manager of a sports store wants 5 different tents to be illustrated on one page of a sales flyer. The illustrations will be positioned one above the other.

In the flyer, the Dome, Rain and Spacious tents are blue, the Scout tent is beige, and the Hiking tent is yellow. The blue tents can appear in any order; however, the manager does not want to have one blue tent immediately after another blue tent. If this is the only restriction, then how many different positions are possible?
A. / 2 / B. / 12 / C. / 20 / D. / 60
2. How many different arrangements consisting of three letters, beginning and ending with different consonants and having a vowel in the middle, can be made with the letters of the word
R E D I A L?
A. / 18 / B. / 20 / C. / 27 / D. / 120
3. Assume a car license plate consists of 7 characters. The first 3 characters can be any of the letters from A to F, but no letter can be repeated. The next 3 characters can be any of the digits from 1 to 9, but no digit can be repeated. The last character can be any of the letters X, Y or Z.
An example of this format is: BFA648Y.
How many license plates are possible?
A. / 5040 / B. / 181 440 / C. / 472 392 / D. / 4 084 080
4. A soccer coach must choose 3 out of 10 players to kick tie-breaking penalty shots. Assuming the coach must designate the order of the 3 players, determine the number of different arrangements she has available.
A. / / B. / / C. / / D. /
5. When you play lotto 5-30, you must choose 5 different integers from 1 to 30. How many
combinations are possible?
A. / / B. / / C. / 25! / D. /
6. If nPr = 3024 and nCr = 126 then the value of r is
A. / 4 / B. / 6 / C. / 9 / D. / 24
7. In how many ways can a gymnastics class of 15 gymnasts be divided into 3 groups so that 3 gymnasts are in one group, 5 gymnasts are in a second group, and 7 gymnasts are in a third group?
A. / 105 / B. / 2 184 / C. / 360 360 / D. / 3 628 800
8. The diagram below illustrates all the chords that can be drawn using the 5 points given on the circumference of a circle.

The number of chords drawn is the same as the number of
A. / arrangements of 5 people in a straight line
B. / arrangements of 5 people sitting at a round table
C. / selections of 2 people from a group of 5 people
D. / selections of 1 person for a certain job and 1 other person for a different job from a group of 5 people
9. The value of aC5, where and a > 5, is equal to the value of
A. / 5Ca / B. / a - 5C5 / C. / aCa - 5 / D. / aC5 - a
10. If all of the letters in the word DIPLOMA are used, then the number of different 7-letter arrangements that can be made beginning with 3 vowels is
A. / 24 / B. / 144 / C. / 720 / D. / 5040
11. There are 45 multiple-choice questions on an exam with 4 possible answers for each question. How many different ways are there to complete the test?
A. / 45 / B. / 148995 / C. / 3575880 / D. / 445
12. A breakfast consists of choosing one item from each category in the following menu:

Juice: apple, orange, grapefruit
Toast: white, whole wheat
Eggs: scrambled, over easy, poached
Beverage: coffee, tea, milk

How many different breakfast mixes are possible?
A. / 11 / B. / 48 / C. / 54 / D. / 96
13. North American area codes are three digit numbers. Before 1980, area codes had the following restrictions, the first digit could not be 0 or 7 or 9, the second digit was either 0 or 1 or 2, and the third digit was any number from 1 through 9 inclusive. Under these rules, how many different area codes were possible?
A. / 112 / B. / 120 / C. / 144 / D. / 147
14. What is the sum of
A. / 8 / B. / 8! / C. / 28 / D. / 88
15. Use the following information to answer the next question.
A children's game consists of a maze through which a marble travels downward, as shown below:

If the marble can enter through any of the 6 entrances, then the total number of different paths that a marble can take through the maze is
A. / 21 / B. / 30 / C. / 32 / D. / 120
16. Use the following information to answer the next question.
A student must draw a path from point A to point B in the diagram below.

If each path much be drawn along the lines such that it is always getting closer to B, then the number of paths that the students can draw is
A. / 12 / B. / 20 / C. / 40 / D. / 70
17. Moving only to the right or down, how many different routes exist to get from point A to point B?

A. / 8 / B. / 7 / C. / 6 / D. / 5
18. Determine the number of different arrangements of all the letters in APPLEPIE.
A. / 3360 / B. / 6720 / C. / 40 312 / D. / 40 320
19. A tune of "Row, Row, Row Your Boat" has 5 notes in its first line:
C C C D E
Assume that all 5 notes are held for the same length of time. If the notes are rearranged at random, how many different melodies could be composed?
A. / 6 / B. / 20 / C. / 40 / D. / 120
20. In how many ways can four cokes, three pepsis, three juices and two jones soda be distributed among 12 graduates if each graduate is to receive one beverage?
A. / 72 / B. / 4200 / C. / 277200 / D. / 3628800
21. Solve for n: nP2 = 56
A. / 56 / B. / 8 / C. / 7 / D. / 2
22. Determine the first three terms in the expansion of (x + 2y)10.
A. / x10 + 10x9y + 90x8y2 / B. / x10 + 20x9y + 180x8y2
C. / x10 + 10x9y + 45x8y2 / D. / x10 + 20x9y + 45x8y2
23. Determine the 5th term in the expansion of

A. / / B. / / C. / / D. /
24. In the expansion of (2x – 1)10 , the coefficient of the term containing x8 is
A. / -11 520 / B. / 45 / C. / 256 / D. / 11 520
25. The binomial expansion of (2x - 3)2n - 1 has 16 terms. The value of n is
A. / 8 / B. / 9 / C. / 15 / D. / 16
26. A teacher requires some help to prepare a bulletin board for the class. There are 26 students in the class.
a) How many different volunteer groups of four students are possible?

b) How many of these groups will include Jim, one of the students in the class?
27. The number of 3-digit numbers less than 400 that can be formed if the last digit is either 4 or 5 is ? .
28. There are five boys and six girls on a grad committee.
a) In how many ways can a sub-committee of two boys and two girls be selected from the committee?

b) In how many ways can a sub-committee of four people be selected if there must be at least one girl on the sub-committee?
29. Sears wants to build 10 new stores in Canada. They have the following information:

If Sears wants to study the desirability of combinations of locations, how many combinations would the company have to consider?
30. From a deck of 52 cards, how many different 5-card hands can be dealt with:
a) exactly 3 clubs

b) at least 2 clubs

c) 3 clubs and 2 spades



d) 2 queens

e) 1 red queen

31.  Solve:





32. Solve algebraically:




33. Correct to the nearest whole number, the value of is ? .


34. For the expansion of (7 - 2x)9
a) find the equation for the general term.



b) find the fifth term of the expansion.