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10 Choose 2

Combination Calculator

What is 10 choose 2?

Answer

10 choose 2 is

45

Order doesn't matter, no repeats: 45 ways to choose 2 of 10 items.

C(10, 2) = 10! / (2! · 8!)

= 45

If order matters (permutations): P(10, 2) = 10 × 9 = 90 — each combination in 2! = 2 orders.

Row 10 of Pascal's triangle
k	10 choose k
0	1
1	10
2	45
3	120
4	210
5	252
6	210
7	120
8	45
9	10
10	1

Row sum: 2¹⁰ = 1,024 — all subsets of 10 items.

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https://calculat.io/en/number/combinations/10--2

<a href="https://calculat.io/en/number/combinations/10--2">10 Choose 2: Combinations C(10, 2) - Calculatio</a>

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10 Choose 2: Combinations C(10, 2). 10 choose 2 = 45: the number of ways to choose 2 of 10 items when order doesn't matter and nothing repeats. C(10, 2) = (10 × 9) / (2 × 1).

https://calculat.io/en/number/combinations/10--2/generated.jpg

n choose 2 for other n

n choose 2	Answer
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
17 choose 2	136

Recalculate with different values ↑

FAQ

What is 10 choose 2?

10 choose 2 is 45

Why is 10 choose 2 the same as 10 choose 8?

Every way to choose 2 of 10 items leaves exactly 8 behind, so choosing 2 and choosing which 8 to leave out are the same count: 10 choose 2 = 10 choose 8 = 45. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(10, 2) = 90. Each of the 45 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.