12 Choose 9

Combination Calculator
Total items (n)
Items chosen (k)

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)

= (12 × 11 × 10) / (3 × 2 × 1)
= 1,320 / 6

= 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
k12 choose k
01
112
266
3220
4495
5792
6924
7792
8495
9220
1066
1112
121

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

See Also

Recalculate with different values ↑

n choose 9 for other n

n choose 9Answer
9 choose 91
10 choose 910
11 choose 955
12 choose 9220
13 choose 9715
14 choose 92,002
15 choose 95,005
16 choose 911,440
17 choose 924,310
18 choose 948,620
19 choose 992,378
20 choose 9167,960

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)!.

See Also