4 Choose 4

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

What is 4 choose 4?

Answer

4 choose 4 is
1

Order doesn't matter, no repeats: 1 way to choose 4 of 4 items.

There is exactly one way: take all.

C(4, 4) = 4! / (4! · 0!)

= 1

0! = 1 (an empty product), so 4! cancels out completely.

If order matters (permutations): P(4, 4) = 4 × 3 × 2 × 1 = 24 — each combination in 4! = 24 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 4 for other n

n choose 4Answer
1 choose 40
2 choose 40
3 choose 40
4 choose 41
5 choose 45
6 choose 415
7 choose 435
8 choose 470
9 choose 4126
10 choose 4210
11 choose 4330
12 choose 4495
13 choose 4715
14 choose 41,001
15 choose 41,365

FAQ

What is 4 choose 4?

4 choose 4 is 1

Why is 4 choose 4 the same as 4 choose 0?

Every way to choose 4 of 4 items leaves exactly 0 behind, so choosing 4 and choosing which 0 to leave out are the same count: 4 choose 4 = 4 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(4, 4) = 24. The only combination — all 4 items — can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also