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13 Choose 13

Combination Calculator

What is 13 choose 13?

Answer

13 choose 13 is

1

Order doesn't matter, no repeats: 1 way to choose 13 of 13 items.

There is exactly one way: take all.

C(13, 13) = 13! / (13! · 0!)

= 1

0! = 1 (an empty product), so 13! cancels out completely.

If order matters (permutations): P(13, 13) = 13 × 12 × 11 × … × 1 = 6,227,020,800 — each combination in 13! = 6,227,020,800 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--13

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

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

https://calculat.io/en/number/combinations/13--13/generated.jpg

n choose 13 for other n

n choose 13	Answer
13 choose 13	1
14 choose 13	14
15 choose 13	105
16 choose 13	560
17 choose 13	2,380
18 choose 13	8,568
19 choose 13	27,132
20 choose 13	77,520

Recalculate with different values ↑

FAQ

What is 13 choose 13?

13 choose 13 is 1

Why is 13 choose 13 the same as 13 choose 0?

Every way to choose 13 of 13 items leaves exactly 0 behind, so choosing 13 and choosing which 0 to leave out are the same count: 13 choose 13 = 13 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(13, 13) = 6,227,020,800. The only combination — all 13 items — can be put in order in 13! = 6,227,020,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.