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14 Choose 14

Combination Calculator

What is 14 choose 14?

Answer

14 choose 14 is

1

Order doesn't matter, no repeats: 1 way to choose 14 of 14 items.

There is exactly one way: take all.

C(14, 14) = 14! / (14! · 0!)

= 1

0! = 1 (an empty product), so 14! cancels out completely.

If order matters (permutations): P(14, 14) = 14 × 13 × 12 × … × 1 = 87,178,291,200 — each combination in 14! = 87,178,291,200 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--14

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

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

https://calculat.io/en/number/combinations/14--14/generated.jpg

n choose 14 for other n

n choose 14	Answer
14 choose 14	1
15 choose 14	15
16 choose 14	120
17 choose 14	680
18 choose 14	3,060
19 choose 14	11,628
20 choose 14	38,760

Recalculate with different values ↑

FAQ

What is 14 choose 14?

14 choose 14 is 1

Why is 14 choose 14 the same as 14 choose 0?

Every way to choose 14 of 14 items leaves exactly 0 behind, so choosing 14 and choosing which 0 to leave out are the same count: 14 choose 14 = 14 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(14, 14) = 87,178,291,200. The only combination — all 14 items — can be put in order in 14! = 87,178,291,200 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.