12 Choose 6

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

What is 12 choose 6?

Answer

12 choose 6 is
924

Order doesn't matter, no repeats: 924 ways to choose 6 of 12 items.

C(12, 6) = 12! / (6! · 6!)

= (12 × 11 × 10 × 9 × 8 × 7) / (6 × 5 × 4 × 3 × 2 × 1)
= 665,280 / 720

= 924

If order matters (permutations): P(12, 6) = 12 × 11 × 10 × 9 × 8 × 7 = 665,280 — each combination in 6! = 720 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 6 for other n

n choose 6Answer
6 choose 61
7 choose 67
8 choose 628
9 choose 684
10 choose 6210
11 choose 6462
12 choose 6924
13 choose 61,716
14 choose 63,003
15 choose 65,005
16 choose 68,008
17 choose 612,376
18 choose 618,564
19 choose 627,132
20 choose 638,760

FAQ

What is 12 choose 6?

12 choose 6 is 924

Why is 12 choose 6 the largest number in row 12?

In row 12 of Pascal's triangle the numbers grow towards the middle and shrink after it, because n choose k = n choose (n − k). With an even n the middle is k = 6, so 12 choose 6 = 924 is the largest: 12 choose 5 is only 792.

How many ways are there if order matters?

P(12, 6) = 665,280. Each of the 924 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also