Advanced Combination Applications

  • 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: 8157 | Total Attempts: 9,569,759
| Questions: 10 | Updated: Dec 10, 2025
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Question 1 / 11
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1) Find C(25, 2)

Explanation

C(25, 2) = 25×24 ÷ 2×1 = 300.

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About This Quiz
Advanced Combination Applications - Quiz

Combinations aren’t just formulas—they solve real-world problems. In this quiz, you’ll apply advanced combination principles to practical and challenging scenarios. Take this quiz to see how counting methods extend to everyday applications.

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2) Find C(15, 12)

Explanation

C(15, 12) = C(15, 3) by symmetry = 455.

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3) Find C(18, 0)

Explanation

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

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4) Find C(17, 2)

Explanation

C(17, 2) = 17×16 ÷ 2×1 = 136.

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5) Find C(12, 10)

Explanation

C(12, 10) = C(12, 2) = 12×11 ÷ 2×1 = 66.

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6) Find C(14, 7)

Explanation

C(14, 7) = 14! ÷ (7!×7!) = 3432.

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7) Find C(19, 3)

Explanation

C(19, 3) = 19×18×17 ÷ 3×2×1 = 969.

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8) Find C(16, 5)

Explanation

C(16, 5) = 16×15×14×13×12 ÷ 5×4×3×2×1 = 4368.

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9) Find C(22, 1)

Explanation

C(n, 1) = n, so 22 choose 1 = 22.

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10) Find C(20, 10)

Explanation

C(20, 10) = 20! ÷ (10!×10!) = 184,756.

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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(25, 2)
Find C(15, 12)
Find C(18, 0)
Find C(17, 2)
Find C(12, 10)
Find C(14, 7)
Find C(19, 3)
Find C(16, 5)
Find C(22, 1)
Find C(20, 10)
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