8 Choose 2

Combination Calculator
Total items (n)
Items chosen (k)

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!)

= (8 × 7) / (2 × 1)
= 56 / 2

= 28

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

Row 8 of Pascal's triangle
k8 choose k
01
18
228
356
470
556
628
78
81

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

See Also

Recalculate with different values ↑

n choose 2 for other n

n choose 2Answer
1 choose 20
2 choose 21
3 choose 23
4 choose 26
5 choose 210
6 choose 215
7 choose 221
8 choose 228
9 choose 236
10 choose 245
11 choose 255
12 choose 266
13 choose 278
14 choose 291
15 choose 2105

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)!.

See Also