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3 Choose 3

Combination Calculator

What is 3 choose 3?

Answer

3 choose 3 is

1

Order doesn't matter, no repeats: 1 way to choose 3 of 3 items.

There is exactly one way: take all.

C(3, 3) = 3! / (3! · 0!)

= 1

0! = 1 (an empty product), so 3! cancels out completely.

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

Row 3 of Pascal's triangle
k	3 choose k
0	1
1	3
2	3
3	1

Row sum: 2³ = 8 — all subsets of 3 items.

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See Also

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https://calculat.io/en/number/combinations/3--3

<a href="https://calculat.io/en/number/combinations/3--3">3 Choose 3: Combinations C(3, 3) - Calculatio</a>

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3 Choose 3: Combinations C(3, 3). 3 choose 3 = 1: the number of ways to choose 3 of 3 items when order doesn't matter and nothing repeats.

https://calculat.io/en/number/combinations/3--3/generated.jpg

n choose 3 for other n

n choose 3	Answer
1 choose 3	0
2 choose 3	0
3 choose 3	1
4 choose 3	4
5 choose 3	10
6 choose 3	20
7 choose 3	35
8 choose 3	56
9 choose 3	84
10 choose 3	120
11 choose 3	165
12 choose 3	220
13 choose 3	286
14 choose 3	364
15 choose 3	455

Recalculate with different values ↑

FAQ

What is 3 choose 3?

3 choose 3 is 1

Why is 3 choose 3 the same as 3 choose 0?

Every way to choose 3 of 3 items leaves exactly 0 behind, so choosing 3 and choosing which 0 to leave out are the same count: 3 choose 3 = 3 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(3, 3) = 6. The only combination — all 3 items — can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.