Combinations Basics

  • 10th Grade
Reviewed by Cierra Henderson
Cierra Henderson, MBA |
K-12 Expert
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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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Thames
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Quizzes Created: 8156 | Total Attempts: 9,588,805
| Attempts: 19 | Questions: 10 | Updated: Jan 20, 2026
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Question 1 / 11
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1) Find 7C1.

Explanation

nC1 = n = 7.

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About This Quiz
Combinations Basics - Quiz

Combinations help us count selections when order doesn’t matter. In this quiz, you’ll practice the fundamentals of combinations, learning how to choose groups from a larger set. Take this quiz to build a solid foundation in counting principles.

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2) Evaluate 5C2.

Explanation

5C2 = 5! / (2! × 3!) = 10.

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3) Find 15C1.

Explanation

nC1 = n = 15.

Submit

4) Find 9C2.

Explanation

9C2 = 9 × 8 / 2 = 36.

Submit

5) Find 12C2.

Explanation

12C2 = 12 × 11 / 2 = 66.

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6) Find 8C3.

Explanation

8C3 = 8! / (3! × 5!) = 56.

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7) Which of the following identities is true for combinations?

Explanation

This is the symmetry property of combinations.

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8) Find 6C3.

Explanation

6C3 = 6! / (3! × 3!) = 20.

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9) Find 8C8.

Explanation

nCn = 1.

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10) Find 10C0.

Explanation

nC0 = 1.

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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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Find 7C1.
Evaluate 5C2.
Find 15C1.
Find 9C2.
Find 12C2.
Find 8C3.
Which of the following identities is true for combinations?
Find 6C3.
Find 8C8.
Find 10C0.
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