12 Choose 3

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

What is 12 choose 3?

Answer

12 choose 3 is
220

Order doesn't matter, no repeats: 220 ways to choose 3 of 12 items.

C(12, 3) = 12! / (3! · 9!)

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

= 220

If order matters (permutations): P(12, 3) = 12 × 11 × 10 = 1,320 — each combination in 3! = 6 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 3 for other n

n choose 3Answer
5 choose 310
6 choose 320
7 choose 335
8 choose 356
9 choose 384
10 choose 3120
11 choose 3165
12 choose 3220
13 choose 3286
14 choose 3364
15 choose 3455
16 choose 3560
17 choose 3680
18 choose 3816
19 choose 3969

FAQ

What is 12 choose 3?

12 choose 3 is 220

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

Every way to choose 3 of 12 items leaves exactly 9 behind, so choosing 3 and choosing which 9 to leave out are the same count: 12 choose 3 = 12 choose 9 = 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, 3) = 1,320. Each of the 220 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also