9 Choose 7
Combination Calculator
What is 9 choose 7?
Answer
9 choose 7 is
36
Order doesn't matter, no repeats: 36 ways to choose 7 of 9 items.
Choosing 7 of 9 is the same as leaving 2 out: C(9, 7) = C(9, 2).
C(9, 7) = 9! / (7! · 2!)
= C(9, 2)
= (9 × 8) / (2 × 1)
= 72 / 2
= 36
If order matters (permutations): P(9, 7) = 9 × 8 × 7 × … × 3 = 181,440 — each combination in 7! = 5,040 orders.
Row sum: 29 = 512 — all subsets of 9 items.
See Also
- Random Number Generator - Pick a random whole number between two bounds
- Percent to Probability Converter - Convert Percents to "1 in X" Probability Chance
- Factors of a Number - List all Factors and Factor Pairs of a Number
n choose 7 for other n
FAQ
What is 9 choose 7?
9 choose 7 is 36
Why is 9 choose 7 the same as 9 choose 2?
Every way to choose 7 of 9 items leaves exactly 2 behind, so choosing 7 and choosing which 2 to leave out are the same count: 9 choose 7 = 9 choose 2 = 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, 7) = 181,440. Each of the 36 combinations can be put in order in 7! = 5,040 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.
See Also
- 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 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 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)
- 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)
- Число сочетаний из 9 по 7
- Combinaciones de 9 tomados de 7 en 7: C(9, 7)
- Combinação de 9 tomados 7 a 7: C(9, 7)