9 Choose 5

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

What is 9 choose 5?

Answer

9 choose 5 is
126

Order doesn't matter, no repeats: 126 ways to choose 5 of 9 items.

Choosing 5 of 9 is the same as leaving 4 out: C(9, 5) = C(9, 4).

C(9, 5) = 9! / (5! · 4!)

= C(9, 4)

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

= 126

If order matters (permutations): P(9, 5) = 9 × 8 × 7 × 6 × 5 = 15,120 — each combination in 5! = 120 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 5 for other n

n choose 5Answer
2 choose 50
5 choose 51
6 choose 56
7 choose 521
8 choose 556
9 choose 5126
10 choose 5252
11 choose 5462
12 choose 5792
13 choose 51,287
14 choose 52,002
15 choose 53,003
16 choose 54,368
17 choose 56,188
18 choose 58,568

FAQ

What is 9 choose 5?

9 choose 5 is 126

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

Every way to choose 5 of 9 items leaves exactly 4 behind, so choosing 5 and choosing which 4 to leave out are the same count: 9 choose 5 = 9 choose 4 = 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, 5) = 15,120. Each of the 126 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also