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11 Choose 2

Combination Calculator

What is 11 choose 2?

Answer

11 choose 2 is

55

Order doesn't matter, no repeats: 55 ways to choose 2 of 11 items.

C(11, 2) = 11! / (2! · 9!)

= 55

If order matters (permutations): P(11, 2) = 11 × 10 = 110 — each combination in 2! = 2 orders.

Row 11 of Pascal's triangle
k	11 choose k
0	1
1	11
2	55
3	165
4	330
5	462
6	462
7	330
8	165
9	55
10	11
11	1

Row sum: 2¹¹ = 2,048 — all subsets of 11 items.

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https://calculat.io/en/number/combinations/11--2

<a href="https://calculat.io/en/number/combinations/11--2">11 Choose 2: Combinations C(11, 2) - Calculatio</a>

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11 Choose 2: Combinations C(11, 2). 11 choose 2 = 55: the number of ways to choose 2 of 11 items when order doesn't matter and nothing repeats. C(11, 2) = (11 × 10) / (2 × 1).

https://calculat.io/en/number/combinations/11--2/generated.jpg

n choose 2 for other n

n choose 2	Answer
4 choose 2	6
5 choose 2	10
6 choose 2	15
7 choose 2	21
8 choose 2	28
9 choose 2	36
10 choose 2	45
11 choose 2	55
12 choose 2	66
13 choose 2	78
14 choose 2	91
15 choose 2	105
16 choose 2	120
17 choose 2	136
18 choose 2	153

Recalculate with different values ↑

FAQ

What is 11 choose 2?

11 choose 2 is 55

Why is 11 choose 2 the same as 11 choose 9?

Every way to choose 2 of 11 items leaves exactly 9 behind, so choosing 2 and choosing which 9 to leave out are the same count: 11 choose 2 = 11 choose 9 = 55. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(11, 2) = 110. Each of the 55 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.