EXAMPLE 3.1.4

1. A student will schedule her classes next semester by choosing one course from each of the following categories:

i. ARH3130, ARH3150, or ARH4110;

ii. STA1013, CGS2030, MGF1107 or MAC1105;

iii. ENC1142, ENC1144, or ENC1145;

iv. WOH1023, WOH1030, AMH1000, EUH2100 or AFH1000.

How many different 4-course combinations are possible?

A. 180
B. 27
C. 15
D. 16

SOLUTION
Choosing a schedule requires her to make four decisions:

i. ARH3130, ARH3150, or ARH4110: 3 options;

ii. STA1013, CGS2030, MGF1107 or MAC1105: 4 options;

iii. ENC1142, ENC1144, or ENC1145: 3 options;

iv. WOH1023, WOH1030, AMH1000, EUH2100 or AFH1000: 5 options.

According to the Fundamental Counting Principle, the number of outcomes is:
(3)(4)(3)(5) = 180


2. How many 4-course combinations are possible if she knows that she can't take ARH4110 and she will take STA1013?

SOLUTION

Again, choosing a schedule requires her to make four decisions. However, some of the decisions are influenced by predetermined conditions:

i. ARH3130, ARH3150, or ARH4110: 2 options;

ii. STA1013, CGS2030, MGF1107 or MAC1105: 1 option;

iii. ENC1142, ENC1144, or ENC1145: 3 options;


iv. WOH1023, WOH1030, AMH1000, EUH2100 or AFH1000: 5 options.

According to the Fundamental Counting Principle, the number of outcomes is:
(2)(1)(3)(5) = 30