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2 Choose 2

Combination Calculator

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
k	2 choose k
0	1
1	2
2	1

Row sum: 2² = 4 — all subsets of 2 items.

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See Also

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

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

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

https://calculat.io/en/number/combinations/2--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 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)!.