Permutations, Combinations, and Counting Principles Quiz

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Quizzes Created: 7387 | Total Attempts: 9,527,684
| Questions: 15 | Updated: Dec 1, 2025
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1) How many ways can you arrange the letters in the word 'LEVEL'?

Explanation

5!/(2!2!)=30.

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About This Quiz
Permutations, Combinations, And Counting Principles Quiz - Quiz

Are you ready to put your foundational combinatorics skills to the test? This quiz will take you through the essential ideas behind counting arrangements, selecting groups, and understanding how order and repetition impact outcomes. You’ll work with real mathematical tasks — from choosing committees to arranging books, distributing objects, and... see moreidentifying when to use permutations vs. combinations. By practicing these core concepts, you’ll gain confidence in solving counting problems step by step and learn how combinatorics helps make sense of decision-making, organization, and structure in everyday math! see less

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2) How many ways can a president and vice-president be chosen from 8 students?

Explanation

8×7=56.

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3) In how many ways can 4 books be arranged on a shelf?

Explanation

4!=24.

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4) Which are examples of combinations?

Explanation

Combinations ignore order.

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5) The number of ways to choose 0 objects from n objects is 1.

Explanation

Empty selection counted once.

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6) How many distinct 5-digit numbers using digits 1–5 without repetition?

Explanation

5!=120.

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7) How many 3-letter words from A,B,C,D if repetition allowed?

Explanation

4^3=64.

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8) Which are true for permutations?

Explanation

Permutations are ordered arrangements.

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9) C(n,r)=C(n,n−r).

Explanation

Choosing r equals excluding n−r.

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10) Distribute 5 identical balls into 3 distinct boxes.

Explanation

C(7,2)=21.

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11) How many 4-digit numbers using digits 1–6 without repetition?

Explanation

6P4=360.

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12) Match: 1.n! 2.C(n,r) 3.n^r

Explanation

Definitions of factorial, combinations, repeated selections.

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13) How many diagonals in convex 8-gon?

Explanation

n(n−3)/2=20.

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14) P(n,r)=n!/(n−r)!

Explanation

Standard permutation formula.

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15) Committee: choose 2 men from 6 and 2 women from 5.

Explanation

15×10=150.

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How many ways can you arrange the letters in the word 'LEVEL'?
How many ways can a president and vice-president be chosen from 8...
In how many ways can 4 books be arranged on a shelf?
Which are examples of combinations?
The number of ways to choose 0 objects from n objects is 1.
How many distinct 5-digit numbers using digits 1–5 without...
How many 3-letter words from A,B,C,D if repetition allowed?
Which are true for permutations?
C(n,r)=C(n,n−r).
Distribute 5 identical balls into 3 distinct boxes.
How many 4-digit numbers using digits 1–6 without repetition?
Match: 1.n! 2.C(n,r) 3.n^r
How many diagonals in convex 8-gon?
P(n,r)=n!/(n−r)!
Committee: choose 2 men from 6 and 2 women from 5.
Alert!

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