3 Choose 2

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

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 / 1

= 3

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

Row 3 of Pascal's triangle
k3 choose k
01
13
23
31

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

See Also