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9 Choose 2

Combination Calculator

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!)

= 36

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

Row 9 of Pascal's triangle
k	9 choose k
0	1
1	9
2	36
3	84
4	126
5	126
6	84
7	36
8	9
9	1

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

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https://calculat.io/en/number/combinations/9--2

<a href="https://calculat.io/en/number/combinations/9--2">9 Choose 2: Combinations C(9, 2) - Calculatio</a>

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9 Choose 2: Combinations C(9, 2). 9 choose 2 = 36: the number of ways to choose 2 of 9 items when order doesn't matter and nothing repeats. C(9, 2) = (9 × 8) / (2 × 1).

https://calculat.io/en/number/combinations/9--2/generated.jpg

n choose 2 for other n

n choose 2	Answer
2 choose 2	1
3 choose 2	3
4 choose 2	6
5 choose 2	10
6 choose 2	15
7 choose 2	21
8 choose 2	28
9 choose 2	36
10 choose 2	45
11 choose 2	55
12 choose 2	66
13 choose 2	78
14 choose 2	91
15 choose 2	105
16 choose 2	120

Recalculate with different values ↑

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)!.