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2 Choose 3

Combination Calculator

What is 2 choose 3?

Answer

2 choose 3 is

0

Order doesn't matter, no repeats: you can't choose 3 items from 2, so there are 0 ways.

3 > 2 → C(2, 3) = 0

If order matters (permutations): P(2, 3) = 0 too.

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.

k = 3 is past the end of row 2.

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

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

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2 Choose 3: Combinations C(2, 3). 2 choose 3 = 0: you can't choose 3 of 2 items without repeats, so there are 0 ways when order doesn't matter.

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

n choose 3 for other n

n choose 3	Answer
1 choose 3	0
2 choose 3	0
3 choose 3	1
4 choose 3	4
5 choose 3	10
6 choose 3	20
7 choose 3	35
8 choose 3	56
9 choose 3	84
10 choose 3	120
11 choose 3	165
12 choose 3	220
13 choose 3	286
14 choose 3	364
15 choose 3	455

Recalculate with different values ↑

FAQ

What is 2 choose 3?

2 choose 3 is 0

Why is 2 choose 3 zero?

You can't pick 3 different items when there are only 2, so there are no ways at all and the answer is 0, not an error. Often the numbers are swapped: 3 choose 2 = 3.

How many ways are there if order matters?

Still none: 3 different items can't be taken from 2 in any order, so P(2, 3) = 0 too.