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2 Choose 10

Combination Calculator

What is 2 choose 10?

Answer

2 choose 10 is

0

Order doesn't matter, no repeats: you can't choose 10 items from 2, so there are 0 ways.

10 > 2 → C(2, 10) = 0

If order matters (permutations): P(2, 10) = 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 = 10 is past the end of row 2.

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https://calculat.io/en/number/combinations/2--10

<a href="https://calculat.io/en/number/combinations/2--10">2 Choose 10: Combinations C(2, 10) - Calculatio</a>

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2 Choose 10: Combinations C(2, 10). 2 choose 10 = 0: you can't choose 10 of 2 items without repeats, so there are 0 ways when order doesn't matter.

https://calculat.io/en/number/combinations/2--10/generated.jpg

n choose 10 for other n

n choose 10	Answer
2 choose 10	0
10 choose 10	1
11 choose 10	11
12 choose 10	66
13 choose 10	286
14 choose 10	1,001
15 choose 10	3,003
16 choose 10	8,008
17 choose 10	19,448
18 choose 10	43,758
19 choose 10	92,378
20 choose 10	184,756
100 choose 10	17,310,309,456,440

Recalculate with different values ↑

FAQ

What is 2 choose 10?

2 choose 10 is 0

Why is 2 choose 10 zero?

You can't pick 10 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: 10 choose 2 = 45.

How many ways are there if order matters?

Still none: 10 different items can't be taken from 2 in any order, so P(2, 10) = 0 too.