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13 Choose 12

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What is 13 choose 12?

Answer

13 choose 12 is

13

Order doesn't matter, no repeats: 13 ways to choose 12 of 13 items.

Choosing 12 of 13 is the same as leaving 1 out: C(13, 12) = C(13, 1).

C(13, 12) = 13! / (12! · 1!)

= C(13, 1)

= 13

If order matters (permutations): P(13, 12) = 13 × 12 × 11 × … × 2 = 6,227,020,800 — each combination in 12! = 479,001,600 orders.

Row 13 of Pascal's triangle
k	13 choose k
0	1
1	13
2	78
3	286
4	715
5	1,287
6	1,716
7	1,716
8	1,287
9	715
10	286
11	78
12	13
13	1

Row sum: 2¹³ = 8,192 — all subsets of 13 items.

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https://calculat.io/en/number/combinations/13--12

<a href="https://calculat.io/en/number/combinations/13--12">13 Choose 12: Combinations C(13, 12) - Calculatio</a>

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13 Choose 12: Combinations C(13, 12). 13 choose 12 = 13: the number of ways to choose 12 of 13 items when order doesn't matter and nothing repeats. C(13, 12) = 13 / 1.

https://calculat.io/en/number/combinations/13--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 13 choose 12?

13 choose 12 is 13

Why is 13 choose 12 the same as 13 choose 1?

Every way to choose 12 of 13 items leaves exactly 1 behind, so choosing 12 and choosing which one to leave out are the same count: 13 choose 12 = 13 choose 1 = 13. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(13, 12) = 6,227,020,800. Each of the 13 combinations can be put in order in 12! = 479,001,600 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.