Combinations Basics (Advanced Pure Math)

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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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Quizzes Created: 8157 | Total Attempts: 9,569,759
| Attempts: 12 | Questions: 10 | Updated: Dec 10, 2025
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Question 1 / 11
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1) Find C(8, 7)

Explanation

Using the identity C(n, n−1) = n, so 8 choose 7 = 8.

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About This Quiz
Combinations Basics (Advanced Pure Math) - Quiz

Go beyond the basics! This quiz dives deeper into combination problems that stretch logical thinking and require more advanced reasoning. Try this quiz to challenge yourself and refine your mastery of pure math applications.

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2) Find C(12, 1)

Explanation

C(n, 1) = n, so 12 choose 1 = 12.

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3) Find C(9, 2)

Explanation

C(9, 2) = 9×8 ÷ 2×1 = 36.

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4) Find C(15, 3)

Explanation

C(15, 3) = 15×14×13 ÷ 3×2×1 = 455.

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5) Find C(11, 4)

Explanation

C(11, 4) = 11×10×9×8 ÷ 4×3×2×1 = 330.

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6) Find C(20, 1)

Explanation

C(n, 1) = n, so 20 choose 1 = 20.

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7) Find C(10, 5)

Explanation

C(10, 5) = 10×9×8×7×6 ÷ 5×4×3×2×1 = 252.

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8) Find C(0, 0)

Explanation

The number of ways to choose 0 items from 0 is 1.

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9) Find C(10, 0)

Explanation

C(n, 0) = 1 for any n.

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10) Find C(13, 13)

Explanation

C(n, n) = 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 C(8, 7)
Find C(12, 1)
Find C(9, 2)
Find C(15, 3)
Find C(11, 4)
Find C(20, 1)
Find C(10, 5)
Find C(0, 0)
Find C(10, 0)
Find C(13, 13)
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