Calculating Basic Permutations

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 18 | Questions: 10 | Updated: Jan 20, 2026
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1) How many permutations are there of 7 distinct books taken all at once?

Explanation

7P7 = 7! = 5040.

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About This Quiz
Calculating Basic Permutations - Quiz

Order matters! In this quiz, you’ll practice calculating simple permutations, learning how to count different arrangements and sequences step by step. Take this quiz to build confidence in tackling arrangement-based problems.

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2) How many ways can 4 students sit in 4 chairs?

Explanation

4P4 = 4! = 24.

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3) How many ways can the letters A, B, C, D be arranged in a line?

Explanation

There are 4P4 = 4! = 24 arrangements.

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4) How many permutations are there of 10 objects taken 1 at a time?

Explanation

10P1 = 10.

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5) In how many ways can 8 runners finish first, second, and third in a race?

Explanation

8P3 = 8 × 7 × 6 = 336.

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6) How many 3-digit codes can be formed from the digits 1–5 if digits cannot repeat?

Explanation

5P3 = 5 × 4 × 3 = 60.

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7) How many permutations are there of 6 objects taken 2 at a time?

Explanation

6P2 = 6 × 5 = 30.

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8) How many permutations are there of 5 objects taken 3 at a time?

Explanation

60 comes from 5P3 = 5 × 4 × 3 = 60.

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9) How many permutations are there of 12 objects taken 2 at a time?

Explanation

12P2 = 12 × 11 = 132.

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10) How many permutations are there of 9 objects taken 3 at a time?

Explanation

9P3 = 9 × 8 × 7 = 504.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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How many permutations are there of 7 distinct books taken all at once?
How many ways can 4 students sit in 4 chairs?
How many ways can the letters A, B, C, D be arranged in a line?
How many permutations are there of 10 objects taken 1 at a time?
In how many ways can 8 runners finish first, second, and third in a...
How many 3-digit codes can be formed from the digits 1–5 if digits...
How many permutations are there of 6 objects taken 2 at a time?
How many permutations are there of 5 objects taken 3 at a time?
How many permutations are there of 12 objects taken 2 at a time?
How many permutations are there of 9 objects taken 3 at a time?
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