9 Choose 2

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

What is 9 choose 2?

Answer

9 choose 2 is
36

Order doesn't matter, no repeats: 36 ways to choose 2 of 9 items.

C(9, 2) = 9! / (2! · 7!)

= (9 × 8) / (2 × 1)
= 72 / 2

= 36

If order matters (permutations): P(9, 2) = 9 × 8 = 72 — each combination in 2! = 2 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 2 for other n

n choose 2Answer
2 choose 21
3 choose 23
4 choose 26
5 choose 210
6 choose 215
7 choose 221
8 choose 228
9 choose 236
10 choose 245
11 choose 255
12 choose 266
13 choose 278
14 choose 291
15 choose 2105
16 choose 2120

FAQ

What is 9 choose 2?

9 choose 2 is 36

Why is 9 choose 2 the same as 9 choose 7?

Every way to choose 2 of 9 items leaves exactly 7 behind, so choosing 2 and choosing which 7 to leave out are the same count: 9 choose 2 = 9 choose 7 = 36. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(9, 2) = 72. Each of the 36 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also