12 Choose 12

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

What is 12 choose 12?

Answer

12 choose 12 is
1

Order doesn't matter, no repeats: 1 way to choose 12 of 12 items.

There is exactly one way: take all.

C(12, 12) = 12! / (12! · 0!)

= 1

0! = 1 (an empty product), so 12! cancels out completely.

If order matters (permutations): P(12, 12) = 12 × 11 × 10 × … × 1 = 479,001,600 — each combination in 12! = 479,001,600 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 12 for other n

n choose 12Answer
12 choose 121
13 choose 1213
14 choose 1291
15 choose 12455
16 choose 121,820
17 choose 126,188
18 choose 1218,564
19 choose 1250,388
20 choose 12125,970

FAQ

What is 12 choose 12?

12 choose 12 is 1

Why is 12 choose 12 the same as 12 choose 0?

Every way to choose 12 of 12 items leaves exactly 0 behind, so choosing 12 and choosing which 0 to leave out are the same count: 12 choose 12 = 12 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(12, 12) = 479,001,600. The only combination — all 12 items — can be put in order in 12! = 479,001,600 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also