2 Choose 2

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

What is 2 choose 2?

Answer

2 choose 2 is
1

Order doesn't matter, no repeats: 1 way to choose 2 of 2 items.

There is exactly one way: take all.

C(2, 2) = 2! / (2! · 0!)

= 1

0! = 1 (an empty product), so 2! cancels out completely.

If order matters (permutations): P(2, 2) = 2 × 1 = 2 — each combination in 2! = 2 orders.

Row 2 of Pascal's triangle
k2 choose k
01
12
21

Row sum: 22 = 4 — all subsets of 2 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 2 choose 2?

2 choose 2 is 1

Why is 2 choose 2 the same as 2 choose 0?

Every way to choose 2 of 2 items leaves exactly 0 behind, so choosing 2 and choosing which 0 to leave out are the same count: 2 choose 2 = 2 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(2, 2) = 2. The only combination — all 2 items — can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also