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14 Choose 13

Combination Calculator

What is 14 choose 13?

Answer

14 choose 13 is

14

Order doesn't matter, no repeats: 14 ways to choose 13 of 14 items.

Choosing 13 of 14 is the same as leaving 1 out: C(14, 13) = C(14, 1).

C(14, 13) = 14! / (13! · 1!)

= C(14, 1)

= 14

If order matters (permutations): P(14, 13) = 14 × 13 × 12 × … × 2 = 87,178,291,200 — each combination in 13! = 6,227,020,800 orders.

Row 14 of Pascal's triangle
k	14 choose k
0	1
1	14
2	91
3	364
4	1,001
5	2,002
6	3,003
7	3,432
8	3,003
9	2,002
10	1,001
11	364
12	91
13	14
14	1

Row sum: 2¹⁴ = 16,384 — all subsets of 14 items.

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See Also

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https://calculat.io/en/number/combinations/14--13

<a href="https://calculat.io/en/number/combinations/14--13">14 Choose 13: Combinations C(14, 13) - Calculatio</a>

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14 Choose 13: Combinations C(14, 13). 14 choose 13 = 14: the number of ways to choose 13 of 14 items when order doesn't matter and nothing repeats. C(14, 13) = 14 / 1.

https://calculat.io/en/number/combinations/14--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 14 choose 13?

14 choose 13 is 14

Why is 14 choose 13 the same as 14 choose 1?

Every way to choose 13 of 14 items leaves exactly 1 behind, so choosing 13 and choosing which one to leave out are the same count: 14 choose 13 = 14 choose 1 = 14. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(14, 13) = 87,178,291,200. Each of the 14 combinations can be put in order in 13! = 6,227,020,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.