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4 Choose 3

Combination Calculator

What is 4 choose 3?

Answer

4 choose 3 is

4

Order doesn't matter, no repeats: 4 ways to choose 3 of 4 items.

Choosing 3 of 4 is the same as leaving 1 out: C(4, 3) = C(4, 1).

C(4, 3) = 4! / (3! · 1!)

= C(4, 1)

= 4

If order matters (permutations): P(4, 3) = 4 × 3 × 2 = 24 — each combination in 3! = 6 orders.

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

Row sum: 2⁴ = 16 — all subsets of 4 items.

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https://calculat.io/en/number/combinations/4--3

<a href="https://calculat.io/en/number/combinations/4--3">4 Choose 3: Combinations C(4, 3) - Calculatio</a>

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4 Choose 3: Combinations C(4, 3). 4 choose 3 = 4: the number of ways to choose 3 of 4 items when order doesn't matter and nothing repeats. C(4, 3) = 4 / 1.

https://calculat.io/en/number/combinations/4--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 4 choose 3?

4 choose 3 is 4

Why is 4 choose 3 the same as 4 choose 1?

Every way to choose 3 of 4 items leaves exactly 1 behind, so choosing 3 and choosing which one to leave out are the same count: 4 choose 3 = 4 choose 1 = 4. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(4, 3) = 24. Each of the 4 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.