18 Choose 6

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

What is 18 choose 6?

Answer

18 choose 6 is
18,564

Order doesn't matter, no repeats: 18,564 ways to choose 6 of 18 items.

C(18, 6) = 18! / (6! · 12!)

= (18 × 17 × 16 × 15 × 14 × 13) / (6 × 5 × 4 × 3 × 2 × 1)
= 13,366,080 / 720

= 18,564

If order matters (permutations): P(18, 6) = 18 × 17 × 16 × 15 × 14 × 13 = 13,366,080 — each combination in 6! = 720 orders.

Row 18 of Pascal's triangle
k18 choose k
01
118
2153
3816
43,060
58,568
618,564
731,824
843,758
948,620
1043,758
1131,824
1218,564
138,568
143,060
15816
16153
1718
181

Row sum: 218 = 262,144 — all subsets of 18 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 18 choose 6?

18 choose 6 is 18,564

Why is 18 choose 6 the same as 18 choose 12?

Every way to choose 6 of 18 items leaves exactly 12 behind, so choosing 6 and choosing which 12 to leave out are the same count: 18 choose 6 = 18 choose 12 = 18,564. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(18, 6) = 13,366,080. Each of the 18,564 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also