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!)
= (10 × 9) / (2 × 1)
= 90 / 2
= 45
If order matters (permutations): P(10, 2) = 10 × 9 = 90 — each combination in 2! = 2 orders.
Row sum: 210 = 1,024 — all subsets of 10 items.
See Also
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n choose 2 for other n
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)!.
See Also
- 9 Choose 2: Combinations C(9, 2)
- 9 Choose 3: Combinations C(9, 3)
- 9 Choose 4: Combinations C(9, 4)
- 9 Choose 5: Combinations C(9, 5)
- 9 Choose 6: Combinations C(9, 6)
- 9 Choose 7: Combinations C(9, 7)
- 9 Choose 8: Combinations C(9, 8)
- 9 Choose 9: Combinations C(9, 9)
- 10 Choose 0: Combinations C(10, 0)
- 10 Choose 1: Combinations C(10, 1)
- 10 Choose 3: Combinations C(10, 3)
- 10 Choose 4: Combinations C(10, 4)
- 10 Choose 5: Combinations C(10, 5)
- 10 Choose 6: Combinations C(10, 6)
- 10 Choose 7: Combinations C(10, 7)
- 10 Choose 8: Combinations C(10, 8)
- 10 Choose 9: Combinations C(10, 9)
- 10 Choose 10: Combinations C(10, 10)
- 11 Choose 0: Combinations C(11, 0)
- 11 Choose 1: Combinations C(11, 1)
- Число сочетаний из 10 по 2
- Combinaciones de 10 tomados de 2 en 2: C(10, 2)
- Combinação de 10 tomados 2 a 2: C(10, 2)