, WGU C960: Discrete Mathematics II
Comprehensive Bank Questions and
Answers with Rationale
Section I: Basic & Advanced Counting
Q1. A passwords consists of 4 distinct letters from the
English alphabet (a-z) followed by 3 distinct digits (0-9).
How many unique passwords can be created?
A) $26^4 \times 10^3$
B) $P(26, 4) \times P(10, 3)$
C) $C(26, 4) \times C(10, 3)$
D) $26 \times 25 \times 24 \times 23 \times 10 \times 10 \times
10$
Key: B
Worked Solution:
Since the characters and digits must be distinct and their
ordering matters, we use permutations.
For the letters: $P(26, 4) = 26 \times 25 \times 24
\times 23 = 358,800$ ways.
Comprehensive Bank Questions and
Answers with Rationale
Section I: Basic & Advanced Counting
Q1. A passwords consists of 4 distinct letters from the
English alphabet (a-z) followed by 3 distinct digits (0-9).
How many unique passwords can be created?
A) $26^4 \times 10^3$
B) $P(26, 4) \times P(10, 3)$
C) $C(26, 4) \times C(10, 3)$
D) $26 \times 25 \times 24 \times 23 \times 10 \times 10 \times
10$
Key: B
Worked Solution:
Since the characters and digits must be distinct and their
ordering matters, we use permutations.
For the letters: $P(26, 4) = 26 \times 25 \times 24
\times 23 = 358,800$ ways.
