12 Choose 4

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

What is 12 choose 4?

Answer

12 choose 4 is
495

Order doesn't matter, no repeats: 495 ways to choose 4 of 12 items.

C(12, 4) = 12! / (4! · 8!)

= (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1)
= 11,880 / 24

= 495

If order matters (permutations): P(12, 4) = 12 × 11 × 10 × 9 = 11,880 — each combination in 4! = 24 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 4 for other n

n choose 4Answer
5 choose 45
6 choose 415
7 choose 435
8 choose 470
9 choose 4126
10 choose 4210
11 choose 4330
12 choose 4495
13 choose 4715
14 choose 41,001
15 choose 41,365
16 choose 41,820
17 choose 42,380
18 choose 43,060
19 choose 43,876

FAQ

What is 12 choose 4?

12 choose 4 is 495

Why is 12 choose 4 the same as 12 choose 8?

Every way to choose 4 of 12 items leaves exactly 8 behind, so choosing 4 and choosing which 8 to leave out are the same count: 12 choose 4 = 12 choose 8 = 495. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(12, 4) = 11,880. Each of the 495 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also