4 Choose 3

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

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 / 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
k4 choose k
01
14
26
34
41

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

See Also