12 Choose 2

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

What is 12 choose 2?

Answer

12 choose 2 is
66

Order doesn't matter, no repeats: 66 ways to choose 2 of 12 items.

C(12, 2) = 12! / (2! · 10!)

= (12 × 11) / (2 × 1)
= 132 / 2

= 66

If order matters (permutations): P(12, 2) = 12 × 11 = 132 — each combination in 2! = 2 orders.

Row 12 of Pascal's triangle
k12 choose k
01
112
266
3220
4495
5792
6924
7792
8495
9220
1066
1112
121

Row sum: 212 = 4,096 — all subsets of 12 items.

See Also

Recalculate with different values ↑

n choose 2 for other n

n choose 2Answer
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
19 choose 2171

FAQ

What is 12 choose 2?

12 choose 2 is 66

Why is 12 choose 2 the same as 12 choose 10?

Every way to choose 2 of 12 items leaves exactly 10 behind, so choosing 2 and choosing which 10 to leave out are the same count: 12 choose 2 = 12 choose 10 = 66. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(12, 2) = 132. Each of the 66 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also