2 Choose 3

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

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
k2 choose k
01
12
21

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

k = 3 is past the end of row 2.

See Also

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.