5 Choose 4

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

What is 5 choose 4?

Answer

5 choose 4 is
5

Order doesn't matter, no repeats: 5 ways to choose 4 of 5 items.

Choosing 4 of 5 is the same as leaving 1 out: C(5, 4) = C(5, 1).

C(5, 4) = 5! / (4! · 1!)

= C(5, 1)

= 5 / 1

= 5

If order matters (permutations): P(5, 4) = 5 × 4 × 3 × 2 = 120 — each combination in 4! = 24 orders.

Row 5 of Pascal's triangle
k5 choose k
01
15
210
310
45
51

Row sum: 25 = 32 — all subsets of 5 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 5 choose 4?

5 choose 4 is 5

Why is 5 choose 4 the same as 5 choose 1?

Every way to choose 4 of 5 items leaves exactly 1 behind, so choosing 4 and choosing which one to leave out are the same count: 5 choose 4 = 5 choose 1 = 5. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(5, 4) = 120. Each of the 5 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also