9 Choose 3
Combination Calculator
What is 9 choose 3?
Answer
9 choose 3 is
84
Order doesn't matter, no repeats: 84 ways to choose 3 of 9 items.
C(9, 3) = 9! / (3! · 6!)
= (9 × 8 × 7) / (3 × 2 × 1)
= 504 / 6
= 84
If order matters (permutations): P(9, 3) = 9 × 8 × 7 = 504 — each combination in 3! = 6 orders.
Row sum: 29 = 512 — all subsets of 9 items.
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n choose 3 for other n
FAQ
What is 9 choose 3?
9 choose 3 is 84
Why is 9 choose 3 the same as 9 choose 6?
Every way to choose 3 of 9 items leaves exactly 6 behind, so choosing 3 and choosing which 6 to leave out are the same count: 9 choose 3 = 9 choose 6 = 84. In the formula n! / (k! (n − k)!) the two factorials below just swap places.
How many ways are there if order matters?
P(9, 3) = 504. Each of the 84 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.
See Also
- 8 Choose 2: Combinations C(8, 2)
- 8 Choose 3: Combinations C(8, 3)
- 8 Choose 4: Combinations C(8, 4)
- 8 Choose 5: Combinations C(8, 5)
- 8 Choose 6: Combinations C(8, 6)
- 8 Choose 7: Combinations C(8, 7)
- 8 Choose 8: Combinations C(8, 8)
- 9 Choose 0: Combinations C(9, 0)
- 9 Choose 1: Combinations C(9, 1)
- 9 Choose 2: Combinations C(9, 2)
- 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 3: Combinations C(10, 3)
- Число сочетаний из 9 по 3
- Combinaciones de 9 tomados de 3 en 3: C(9, 3)
- Combinação de 9 tomados 3 a 3: C(9, 3)