how to succeed in math

Math 30-1

Diploma Prep

Review

Diploma Prep

Review
Solutions

Permutations and Combinations
I. Multiple Choice

Math 30-1
Permutations and Combinations

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.

Multiple Choice
D
C
B
B
B
A
C
B
B
C
D
A
B
B

15. A

1.
2.
3.
4.
5.

Numerical Response
54
126
240
450
2160

Written Response
1. a) i) 27 405 ii) 24 360 iii) 1900 iv) 115 254
b) i) 2520 ii) 420
2. a) n = 16
b)

x7  14x 6 y1  84x5 y 2

Math 30-1

Diploma Prep

Review
Solutions

Permutations and Combinations
I. Multiple Choice
1. A couple is planning an evening out. They have a choice of 4 restaurants for dinner,
6 movies following dinner, and 4 coffee establishments for after the movie. How many different ways can they plan the evening if they choose one of each?
A. 6
B. 14

4 × 6 × 4 = 96

C. 48
D. 96

2. A man has 7 different pets and wishes to photograph them 3 at a time arranged in a line.
How many different arrangements are possible?
A. 21
B. 35

7P3

= 210

C. 210
D. 840

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 from1 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. 5 040
B. 181 440
C. 472 392
D. 4 084 080

6 × 5 × 4 × 9 × 8 × 7 × 3 = 181 440

4. Twelve buttons differ only by colour. There are 4 red buttons, 4 green buttons and 4 yellow buttons. If the buttons are placed in a row, how many different arrangements are possible?
A. 11 880
B. 34 650

12!
 34650
4!4!4!

C. 19 958 400
D. 479 001 600

5. How many odd 3-digit whole numbers are there?
For example, 203 is acceptable but 023 is not.
A. 360
B. 450

9 × 10 × 5 = 450

C. 500
D. 900

6.