9 Choose 4

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

What is 9 choose 4?

Answer

9 choose 4 is
126

Order doesn't matter, no repeats: 126 ways to choose 4 of 9 items.

C(9, 4) = 9! / (4! · 5!)

= (9 × 8 × 7 × 6) / (4 × 3 × 2 × 1)
= 3,024 / 24

= 126

If order matters (permutations): P(9, 4) = 9 × 8 × 7 × 6 = 3,024 — each combination in 4! = 24 orders.

Row 9 of Pascal's triangle
k9 choose k
01
19
236
384
4126
5126
684
736
89
91

Row sum: 29 = 512 — all subsets of 9 items.

See Also

Recalculate with different values ↑

n choose 4 for other n

n choose 4Answer
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
16 choose 41,820

FAQ

What is 9 choose 4?

9 choose 4 is 126

Why is 9 choose 4 the same as 9 choose 5?

Every way to choose 4 of 9 items leaves exactly 5 behind, so choosing 4 and choosing which 5 to leave out are the same count: 9 choose 4 = 9 choose 5 = 126. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(9, 4) = 3,024. Each of the 126 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also