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3 Choose 2

Combination Calculator

What is 3 choose 2?

Answer

3 choose 2 is

3

Order doesn't matter, no repeats: 3 ways to choose 2 of 3 items.

Choosing 2 of 3 is the same as leaving 1 out: C(3, 2) = C(3, 1).

C(3, 2) = 3! / (2! · 1!)

= C(3, 1)

= 3

If order matters (permutations): P(3, 2) = 3 × 2 = 6 — each combination in 2! = 2 orders.

Row 3 of Pascal's triangle
k	3 choose k
0	1
1	3
2	3
3	1

Row sum: 2³ = 8 — all subsets of 3 items.

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https://calculat.io/en/number/combinations/3--2

<a href="https://calculat.io/en/number/combinations/3--2">3 Choose 2: Combinations C(3, 2) - Calculatio</a>

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3 Choose 2: Combinations C(3, 2). 3 choose 2 = 3: the number of ways to choose 2 of 3 items when order doesn't matter and nothing repeats. C(3, 2) = 3 / 1.

https://calculat.io/en/number/combinations/3--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 3 choose 2?

3 choose 2 is 3

Why is 3 choose 2 the same as 3 choose 1?

Every way to choose 2 of 3 items leaves exactly 1 behind, so choosing 2 and choosing which one to leave out are the same count: 3 choose 2 = 3 choose 1 = 3. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(3, 2) = 6. Each of the 3 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.