18 Choose 12

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

What is 18 choose 12?

Answer

18 choose 12 is
18,564

Order doesn't matter, no repeats: 18,564 ways to choose 12 of 18 items.

Choosing 12 of 18 is the same as leaving 6 out: C(18, 12) = C(18, 6).

C(18, 12) = 18! / (12! · 6!)

= C(18, 6)

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

= 18,564

If order matters (permutations): P(18, 12) = 18 × 17 × 16 × … × 7 = 8,892,185,702,400 — each combination in 12! = 479,001,600 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 12 for other n

n choose 12Answer
12 choose 121
13 choose 1213
14 choose 1291
15 choose 12455
16 choose 121,820
17 choose 126,188
18 choose 1218,564
19 choose 1250,388
20 choose 12125,970

FAQ

What is 18 choose 12?

18 choose 12 is 18,564

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

Every way to choose 12 of 18 items leaves exactly 6 behind, so choosing 12 and choosing which 6 to leave out are the same count: 18 choose 12 = 18 choose 6 = 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, 12) = 8,892,185,702,400. Each of the 18,564 combinations can be put in order in 12! = 479,001,600 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also