3 Choose 3

Combination Calculator
Total items (n)
Items chosen (k)

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
k3 choose k
01
13
23
31

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

See Also

Recalculate with different values ↑

n choose 3 for other n

n choose 3Answer
1 choose 30
2 choose 30
3 choose 31
4 choose 34
5 choose 310
6 choose 320
7 choose 335
8 choose 356
9 choose 384
10 choose 3120
11 choose 3165
12 choose 3220
13 choose 3286
14 choose 3364
15 choose 3455

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)!.

See Also