6 Choose 2

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

What is 6 choose 2?

Answer

6 choose 2 is
15

Order doesn't matter, no repeats: 15 ways to choose 2 of 6 items.

C(6, 2) = 6! / (2! · 4!)

= (6 × 5) / (2 × 1)
= 30 / 2

= 15

If order matters (permutations): P(6, 2) = 6 × 5 = 30 — each combination in 2! = 2 orders.

Row 6 of Pascal's triangle
k6 choose k
01
16
215
320
415
56
61

Row sum: 26 = 64 — all subsets of 6 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 6 choose 2?

6 choose 2 is 15

Why is 6 choose 2 the same as 6 choose 4?

Every way to choose 2 of 6 items leaves exactly 4 behind, so choosing 2 and choosing which 4 to leave out are the same count: 6 choose 2 = 6 choose 4 = 15. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(6, 2) = 30. Each of the 15 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also