6 Choose 4

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

What is 6 choose 4?

Answer

6 choose 4 is
15

Order doesn't matter, no repeats: 15 ways to choose 4 of 6 items.

Choosing 4 of 6 is the same as leaving 2 out: C(6, 4) = C(6, 2).

C(6, 4) = 6! / (4! · 2!)

= C(6, 2)

= (6 × 5) / (2 × 1)
= 30 / 2

= 15

If order matters (permutations): P(6, 4) = 6 × 5 × 4 × 3 = 360 — each combination in 4! = 24 orders.

Row 6 of Pascal's triangle
k6 choose k
01
16
215
320
415
56
61

Row sum: 26 = 64 — all subsets of 6 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 6 choose 4?

6 choose 4 is 15

Why is 6 choose 4 the same as 6 choose 2?

Every way to choose 4 of 6 items leaves exactly 2 behind, so choosing 4 and choosing which 2 to leave out are the same count: 6 choose 4 = 6 choose 2 = 15. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(6, 4) = 360. Each of the 15 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also