10 Choose 3
Combination Calculator
What is 10 choose 3?
Answer
10 choose 3 is
120
Order doesn't matter, no repeats: 120 ways to choose 3 of 10 items.
C(10, 3) = 10! / (3! · 7!)
= (10 × 9 × 8) / (3 × 2 × 1)
= 720 / 6
= 120
If order matters (permutations): P(10, 3) = 10 × 9 × 8 = 720 — each combination in 3! = 6 orders.
Row sum: 210 = 1,024 — all subsets of 10 items.
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n choose 3 for other n
FAQ
What is 10 choose 3?
10 choose 3 is 120
Why is 10 choose 3 the same as 10 choose 7?
Every way to choose 3 of 10 items leaves exactly 7 behind, so choosing 3 and choosing which 7 to leave out are the same count: 10 choose 3 = 10 choose 7 = 120. In the formula n! / (k! (n − k)!) the two factorials below just swap places.
How many ways are there if order matters?
P(10, 3) = 720. Each of the 120 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.
See Also
- 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 2: Combinations C(10, 2)
- 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)
- 11 Choose 2: Combinations C(11, 2)
- Число сочетаний из 10 по 3
- Combinaciones de 10 tomados de 3 en 3: C(10, 3)
- Combinação de 10 tomados 3 a 3: C(10, 3)