Practice Questions
Concept Explanation
The fundamental counting principle states that if one event can occur in m ways and a second independent event in n ways, both together can occur in m × n ways.
Key Rules
- Multiplication rule (AND): total = m × n × …
- Addition rule (OR, mutually exclusive): total = m + n
- Applies when choices are independent and sequential
Example
4 shirts and 5 trousers give 4 × 5 = 20 outfits.
Common Trap
Use addition only when choices are mutually exclusive (either/or), not when both are required.
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Q1 Easy
A person has 4 shirts and 5 trousers. How many different outfits can be formed?
ExplanationMultiplication rule: 4 × 5 = 20 outfits. -
Q2 Easy
From X to Y there are 3 routes, and from Y to Z there are 4 routes. How many ways to travel from X to Z via Y?
Explanation3 × 4 = 12 routes. -
Q3 Medium
A meal has one appetizer (6), one main (8), and one dessert (4). How many meals are possible?
Explanation6 × 8 × 4 = 192 meals. -
Q4 Easy
A 3-digit code uses digits 0–9 on each of 3 dials. How many codes are possible?
Explanation10 × 10 × 10 = 1000 codes. -
Q5 Medium
A chair is chosen from 7 candidates and a secretary from 5 others. How many ways?
Explanation7 × 5 = 35 ways. -
Q6 Easy
A true/false test has 6 questions. How many answer sheets are possible?
Explanation2^6 = 64 answer sheets. -
Q7 Easy
Rolling a fair die and tossing a coin gives how many outcomes?
Explanation6 × 2 = 12 outcomes.
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Q8 Hard
A password has 2 letters (A–Z) followed by 2 digits (0–9). How many passwords?
Explanation26^2 × 10^2 = 676 × 100 = 67600. -
Q9 Easy
Either a math book (4 titles) or a science book (6 titles) can be read. How many choices?
ExplanationAddition rule: 4 + 6 = 10 choices. -
Q10 Medium
A vehicle comes in 3 colours, 5 models, and 2 engine types. How many variants?
Explanation3 × 5 × 2 = 30 variants. -
Q11 Easy
Three switches, each ON or OFF. How many total switch settings?
Explanation2^3 = 8 settings. -
Q12 Medium
From A to B: 2 roads; B to C: 3 roads; C to D: 2 roads. Ways from A to D via B and C?
Explanation2 × 3 × 2 = 12 ways. -
Q13 Medium
A 2-digit number: tens digit from {1,2,3,4,5} and units digit from {0–9}. How many numbers?
Explanation5 × 10 = 50 numbers. -
Q14 Hard
License plates: 2 letters (26 each) and 3 digits (10 each). How many plates?
Explanation26^2 × 10^3 = 676 × 1000 = 6760000.
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DS1 Easy
How many different outfits can be formed?
Statement IThere are 4 shirts and 5 trousers.
Statement IIEach outfit uses one shirt and one trouser.
ExplanationEach statement alone: 4 × 5 = 20 outfits. -
DS2 Easy
How many ways to travel from P to R via Q?
Statement IFrom P to Q there are 3 routes.
Statement IIFrom Q to R there are 5 routes.
ExplanationNeed both: 3 × 5 = 15 ways.
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DS3 Medium
How many meals can be ordered?
Statement IThere are 5 appetizers and 6 main courses.
Statement IIEach meal includes one appetizer, one main course, and one of 3 desserts.
ExplanationStatement II alone: 5 × 6 × 3 = 90 meals. -
DS4 Easy
How many answer sheets are possible on a true/false quiz?
Statement IThe quiz has 8 questions.
Statement IIEach question has exactly 2 answer choices.
ExplanationEach alone gives 2^8 = 256 answer sheets.