12 Choose 11

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

What is 12 choose 11?

Answer

12 choose 11 is
12

Order doesn't matter, no repeats: 12 ways to choose 11 of 12 items.

Choosing 11 of 12 is the same as leaving 1 out: C(12, 11) = C(12, 1).

C(12, 11) = 12! / (11! · 1!)

= C(12, 1)

= 12 / 1

= 12

If order matters (permutations): P(12, 11) = 12 × 11 × 10 × … × 2 = 479,001,600 — each combination in 11! = 39,916,800 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 11 for other n

n choose 11Answer
11 choose 111
12 choose 1112
13 choose 1178
14 choose 11364
15 choose 111,365
16 choose 114,368
17 choose 1112,376
18 choose 1131,824
19 choose 1175,582
20 choose 11167,960

FAQ

What is 12 choose 11?

12 choose 11 is 12

Why is 12 choose 11 the same as 12 choose 1?

Every way to choose 11 of 12 items leaves exactly 1 behind, so choosing 11 and choosing which one to leave out are the same count: 12 choose 11 = 12 choose 1 = 12. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(12, 11) = 479,001,600. Each of the 12 combinations can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also