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6 Choose 6

Combination Calculator

What is 6 choose 6?

Answer

6 choose 6 is

1

Order doesn't matter, no repeats: 1 way to choose 6 of 6 items.

There is exactly one way: take all.

C(6, 6) = 6! / (6! · 0!)

= 1

0! = 1 (an empty product), so 6! cancels out completely.

If order matters (permutations): P(6, 6) = 6 × 5 × 4 × 3 × 2 × 1 = 720 — each combination in 6! = 720 orders.

Row 6 of Pascal's triangle
k	6 choose k
0	1
1	6
2	15
3	20
4	15
5	6
6	1

Row sum: 2⁶ = 64 — all subsets of 6 items.

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See Also

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https://calculat.io/en/number/combinations/6--6

<a href="https://calculat.io/en/number/combinations/6--6">6 Choose 6: Combinations C(6, 6) - Calculatio</a>

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6 Choose 6: Combinations C(6, 6). 6 choose 6 = 1: the number of ways to choose 6 of 6 items when order doesn't matter and nothing repeats.

https://calculat.io/en/number/combinations/6--6/generated.jpg

n choose 6 for other n

n choose 6	Answer
6 choose 6	1
7 choose 6	7
8 choose 6	28
9 choose 6	84
10 choose 6	210
11 choose 6	462
12 choose 6	924
13 choose 6	1,716
14 choose 6	3,003
15 choose 6	5,005
16 choose 6	8,008
17 choose 6	12,376
18 choose 6	18,564
19 choose 6	27,132
20 choose 6	38,760

Recalculate with different values ↑

FAQ

What is 6 choose 6?

6 choose 6 is 1

Why is 6 choose 6 the same as 6 choose 0?

Every way to choose 6 of 6 items leaves exactly 0 behind, so choosing 6 and choosing which 0 to leave out are the same count: 6 choose 6 = 6 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(6, 6) = 720. The only combination — all 6 items — can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.