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Math › Combinatorics › Combinations › Combination Basics

Combinations Basics (Advanced Pure Math)

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| By Thames

T

Thames

Community Contributor

Quizzes Created: 7049 | Total Attempts: 9,519,298

| Questions: 10

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Question 1 / 10

0 %

0/100

Score 0/100

1) Find C(0, 0)

0

1

Undefined

0.5

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

Explanation

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

Submit

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(8, 7)

1

7

8

56

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

Explanation

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

Submit

3) Find C(10, 0)

0

1

10

100

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

Explanation

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

Submit

4) Find C(12, 1)

1

10

11

12

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

Explanation

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

Submit

5) Find C(9, 2)

36

45

72

54

C(9, 2) = 9×8 ÷ 2×1 = 36.

Explanation

C(9, 2) = 9×8 ÷ 2×1 = 36.

Submit

6) Find C(15, 3)

455

560

2730

1365

C(15, 3) = 15×14×13 ÷ 3×2×1 = 455.

Explanation

C(15, 3) = 15×14×13 ÷ 3×2×1 = 455.

Submit

7) Find C(11, 4)

210

330

440

385

C(11, 4) = 11×10×9×8 ÷ 4×3×2×1 = 330.

Explanation

C(11, 4) = 11×10×9×8 ÷ 4×3×2×1 = 330.

Submit

8) Find C(20, 1)

19

20

21

1

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

Explanation

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

Submit

9) Find C(13, 13)

0

13

1

169

C(n, n) = 1.

Explanation

C(n, n) = 1.

Submit

10) Find C(10, 5)

120

200

240

252

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

Explanation

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

Submit

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Current Version
Oct 13, 2025

Quiz Edited by
ProProfs Editorial Team
Oct 07, 2025

Quiz Created by
Thames

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All (10)
Unanswered ()
Answered ()

Find C(0, 0)

Find C(8, 7)

Find C(10, 0)

Find C(12, 1)

Find C(9, 2)

Find C(15, 3)

Find C(11, 4)

Find C(20, 1)

Find C(13, 13)

Find C(10, 5)

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