Practice Questions
Concept Explanation
Combinations count selections where order does not matter. Choosing r objects from n distinct objects gives nCr.
Key Formulas
- nCr = n! / (r! (n − r)!)
- nCr = nC(n − r)
- nC0 = nCn = 1
Example
8C3 = 8!/(3!×5!) = 56.
Common Trap
Use nCr when order does not matter; nPr when order matters.
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Q1 Easy
How many ways to choose 2 items from 6?
Explanation6C2 = 15. -
Q2 Medium
8C3 equals:
Explanation8C3 = 56. -
Q3 Medium
How many ways to select a team of 3 from 10 players?
Explanation10C3 = 120. -
Q4 Easy
10C2 equals:
Explanation10C2 = 45. -
Q5 Medium
7C4 equals:
Explanation7C4 = 7C3 = 35. -
Q6 Easy
How many ways to choose 1 item from 9?
Explanation9C1 = 9. -
Q7 Medium
12C2 equals:
Explanation12C2 = 66.
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Q8 Medium
How many subsets of a 5-element set?
Explanation2^5 = 32 subsets. -
Q9 Easy
9C0 equals:
Explanation9C0 = 1. -
Q10 Hard
How many ways to select 4 cards from 52? (order irrelevant)
Explanation52C4 = 270725. -
Q11 Easy
6C3 equals:
Explanation6C3 = 20. -
Q12 Medium
11C2 equals:
Explanation11C2 = 55. -
Q13 Easy
How many ways to choose 3 mangoes from 7?
Explanation7C3 = 35. -
Q14 Easy
15C1 equals:
Explanation15C1 = 15.
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DS1 Easy
How many ways to choose 3 items from 8?
Statement IOrder does not matter.
Statement IINo item is chosen more than once.
ExplanationStatement I alone: 8C3 = 56. -
DS2 Easy
What is nCr?
Statement In = 10 and r = 4.
Statement IInCr = 210.
ExplanationEach gives 10C4 = 210.
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DS3 Medium
How many 2-person teams from 9 people?
Statement ITeams are unordered.
Statement IIEach team has exactly 2 members.
ExplanationEach alone: 9C2 = 36. -
DS4 Easy
Is nCr equal to nC(n−r)?
Statement In = 8 and r = 3.
Statement IIn = 8 and (n−r) = 5.
ExplanationEach shows 8C3 = 8C5 = 56.