2 Choose 10

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

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
k2 choose k
01
12
21

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

k = 10 is past the end of row 2.

See Also

Recalculate with different values ↑

n choose 10 for other n

n choose 10Answer
2 choose 100
10 choose 101
11 choose 1011
12 choose 1066
13 choose 10286
14 choose 101,001
15 choose 103,003
16 choose 108,008
17 choose 1019,448
18 choose 1043,758
19 choose 1092,378
20 choose 10184,756
100 choose 1017,310,309,456,440

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.

See Also