11 Choose 2

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

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!)

= (11 × 10) / (2 × 1)
= 110 / 2

= 55

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

Row 11 of Pascal's triangle
k11 choose k
01
111
255
3165
4330
5462
6462
7330
8165
955
1011
111

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

See Also

Recalculate with different values ↑

n choose 2 for other n

n choose 2Answer
4 choose 26
5 choose 210
6 choose 215
7 choose 221
8 choose 228
9 choose 236
10 choose 245
11 choose 255
12 choose 266
13 choose 278
14 choose 291
15 choose 2105
16 choose 2120
17 choose 2136
18 choose 2153

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)!.

See Also