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12 Choose 9

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What is 12 choose 9?

Answer

12 choose 9 is

220

Order doesn't matter, no repeats: 220 ways to choose 9 of 12 items.

Choosing 9 of 12 is the same as leaving 3 out: C(12, 9) = C(12, 3).

C(12, 9) = 12! / (9! · 3!)

= C(12, 3)

= 220

If order matters (permutations): P(12, 9) = 12 × 11 × 10 × … × 4 = 79,833,600 — each combination in 9! = 362,880 orders.

Row 12 of Pascal's triangle
k	12 choose k
0	1
1	12
2	66
3	220
4	495
5	792
6	924
7	792
8	495
9	220
10	66
11	12
12	1

Row sum: 2¹² = 4,096 — all subsets of 12 items.

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https://calculat.io/en/number/combinations/12--9

<a href="https://calculat.io/en/number/combinations/12--9">12 Choose 9: Combinations C(12, 9) - Calculatio</a>

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12 Choose 9: Combinations C(12, 9). 12 choose 9 = 220: the number of ways to choose 9 of 12 items when order doesn't matter and nothing repeats. C(12, 9) = (12 × 11 × 10) / (3 × 2 × 1).

https://calculat.io/en/number/combinations/12--9/generated.jpg

n choose 9 for other n

n choose 9	Answer
9 choose 9	1
10 choose 9	10
11 choose 9	55
12 choose 9	220
13 choose 9	715
14 choose 9	2,002
15 choose 9	5,005
16 choose 9	11,440
17 choose 9	24,310
18 choose 9	48,620
19 choose 9	92,378
20 choose 9	167,960

Recalculate with different values ↑

FAQ

What is 12 choose 9?

12 choose 9 is 220

Why is 12 choose 9 the same as 12 choose 3?

Every way to choose 9 of 12 items leaves exactly 3 behind, so choosing 9 and choosing which 3 to leave out are the same count: 12 choose 9 = 12 choose 3 = 220. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(12, 9) = 79,833,600. Each of the 220 combinations can be put in order in 9! = 362,880 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.