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12 Choose 12

Combination Calculator

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
k	12 choose k
0	1
1	12
2	66
3	220
4	495
5	792
6	924
7	792
8	495
9	220
10	66
11	12
12	1

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

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See Also

Random Number Generator - Pick a random whole number between two bounds
Percent to Probability Converter - Convert Percents to "1 in X" Probability Chance
Factors of a Number - List all Factors and Factor Pairs of a Number

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https://calculat.io/en/number/combinations/12--12

<a href="https://calculat.io/en/number/combinations/12--12">12 Choose 12: Combinations C(12, 12) - Calculatio</a>

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12 Choose 12: Combinations C(12, 12). 12 choose 12 = 1: the number of ways to choose 12 of 12 items when order doesn't matter and nothing repeats.

https://calculat.io/en/number/combinations/12--12/generated.jpg

n choose 12 for other n

n choose 12	Answer
12 choose 12	1
13 choose 12	13
14 choose 12	91
15 choose 12	455
16 choose 12	1,820
17 choose 12	6,188
18 choose 12	18,564
19 choose 12	50,388
20 choose 12	125,970

Recalculate with different values ↑

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)!.