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8 Choose 2

Combination Calculator

What is 8 choose 2?

Answer

8 choose 2 is

28

Order doesn't matter, no repeats: 28 ways to choose 2 of 8 items.

C(8, 2) = 8! / (2! · 6!)

= 28

If order matters (permutations): P(8, 2) = 8 × 7 = 56 — each combination in 2! = 2 orders.

Row 8 of Pascal's triangle
k	8 choose k
0	1
1	8
2	28
3	56
4	70
5	56
6	28
7	8
8	1

Row sum: 2⁸ = 256 — all subsets of 8 items.

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https://calculat.io/en/number/combinations/8--2

<a href="https://calculat.io/en/number/combinations/8--2">8 Choose 2: Combinations C(8, 2) - Calculatio</a>

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8 Choose 2: Combinations C(8, 2). 8 choose 2 = 28: the number of ways to choose 2 of 8 items when order doesn't matter and nothing repeats. C(8, 2) = (8 × 7) / (2 × 1).

https://calculat.io/en/number/combinations/8--2/generated.jpg

n choose 2 for other n

n choose 2	Answer
1 choose 2	0
2 choose 2	1
3 choose 2	3
4 choose 2	6
5 choose 2	10
6 choose 2	15
7 choose 2	21
8 choose 2	28
9 choose 2	36
10 choose 2	45
11 choose 2	55
12 choose 2	66
13 choose 2	78
14 choose 2	91
15 choose 2	105

Recalculate with different values ↑

FAQ

What is 8 choose 2?

8 choose 2 is 28

Why is 8 choose 2 the same as 8 choose 6?

Every way to choose 2 of 8 items leaves exactly 6 behind, so choosing 2 and choosing which 6 to leave out are the same count: 8 choose 2 = 8 choose 6 = 28. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(8, 2) = 56. Each of the 28 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.