Page 1 of 112
Finite Mathematics Full Real Exam |
Questions & Answers with Step-by-Step
Rationales | Probability, Matrices, Sequences,
Series, Finance & Linear Programming (2025
Edition)
Question 1
A survey of 100 dog owners found that 60 own a Labrador, 40
own a Poodle, and 20 own both. How many own neither?
A. 20
B. 30
C. 40
D. 50
Correct Answer: A
,Page 2 of 112
Rationale: Use inclusion-exclusion: |L ∪ P| = |L| + |P| – |L ∩
P| = 60 + 40 – 20 = 80. Neither = total – 80 = 100 – 80 =
20.
Scenario: A pet store analyzes customer preferences. If 80 out of
100 customers own at least one of the two breeds, 20 own
neither.
Question 2
How many distinct 3-letter sequences can be formed from the
letters of the word “MATH”?
A. 4
B. 12
C. 24
D. 64
Correct Answer: C
,Page 3 of 112
Rationale: The number of permutations of 4 distinct letters taken
3 at a time is P(4,3) = 4×3×2 = 24.
Scenario: A security code consists of three different letters from
“MATH”. There are 24 possible codes.
Question 3
In how many ways can a committee of 4 be chosen from 10
people?
A. 210
B. 5040
C. 2100
D. 10000
Correct Answer: A
Rationale: Number of combinations: C(10,4) = 10!/(4!6!) =
(10×9×8×7)/(4×3×2×1) = 5040/24 = 210.
, Page 4 of 112
Scenario: A company selects 4 employees from 10 to form a
safety committee. There are 210 possible committees.
Question 4
A bag contains 5 red, 3 blue, and 2 green marbles. Two marbles
are drawn without replacement. What is the probability that
both are red?
A. 5/10 × 4/9 = 20/90 = 2/9
B. 5/10 × 5/10 = 1/4
C. (5/10)² = 1/4
D. 5/10 × 5/9 = 25/90
Correct Answer: A
Rationale: Probability first red = 5/10, then second red = 4/9.
Multiply: 20/90 = 2/9.
Finite Mathematics Full Real Exam |
Questions & Answers with Step-by-Step
Rationales | Probability, Matrices, Sequences,
Series, Finance & Linear Programming (2025
Edition)
Question 1
A survey of 100 dog owners found that 60 own a Labrador, 40
own a Poodle, and 20 own both. How many own neither?
A. 20
B. 30
C. 40
D. 50
Correct Answer: A
,Page 2 of 112
Rationale: Use inclusion-exclusion: |L ∪ P| = |L| + |P| – |L ∩
P| = 60 + 40 – 20 = 80. Neither = total – 80 = 100 – 80 =
20.
Scenario: A pet store analyzes customer preferences. If 80 out of
100 customers own at least one of the two breeds, 20 own
neither.
Question 2
How many distinct 3-letter sequences can be formed from the
letters of the word “MATH”?
A. 4
B. 12
C. 24
D. 64
Correct Answer: C
,Page 3 of 112
Rationale: The number of permutations of 4 distinct letters taken
3 at a time is P(4,3) = 4×3×2 = 24.
Scenario: A security code consists of three different letters from
“MATH”. There are 24 possible codes.
Question 3
In how many ways can a committee of 4 be chosen from 10
people?
A. 210
B. 5040
C. 2100
D. 10000
Correct Answer: A
Rationale: Number of combinations: C(10,4) = 10!/(4!6!) =
(10×9×8×7)/(4×3×2×1) = 5040/24 = 210.
, Page 4 of 112
Scenario: A company selects 4 employees from 10 to form a
safety committee. There are 210 possible committees.
Question 4
A bag contains 5 red, 3 blue, and 2 green marbles. Two marbles
are drawn without replacement. What is the probability that
both are red?
A. 5/10 × 4/9 = 20/90 = 2/9
B. 5/10 × 5/10 = 1/4
C. (5/10)² = 1/4
D. 5/10 × 5/9 = 25/90
Correct Answer: A
Rationale: Probability first red = 5/10, then second red = 4/9.
Multiply: 20/90 = 2/9.
