18 Choose 11

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

What is 18 choose 11?

Answer

18 choose 11 is
31,824

Order doesn't matter, no repeats: 31,824 ways to choose 11 of 18 items.

Choosing 11 of 18 is the same as leaving 7 out: C(18, 11) = C(18, 7).

C(18, 11) = 18! / (11! · 7!)

= C(18, 7)

= (18 × 17 × 16 × … × 12) / (7 × 6 × 5 × … × 1)

7 factors on top and bottom

= 160,392,960 / 5,040

= 31,824

If order matters (permutations): P(18, 11) = 18 × 17 × 16 × … × 8 = 1,270,312,243,200 — each combination in 11! = 39,916,800 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 11 for other n

n choose 11Answer
11 choose 111
12 choose 1112
13 choose 1178
14 choose 11364
15 choose 111,365
16 choose 114,368
17 choose 1112,376
18 choose 1131,824
19 choose 1175,582
20 choose 11167,960

FAQ

What is 18 choose 11?

18 choose 11 is 31,824

Why is 18 choose 11 the same as 18 choose 7?

Every way to choose 11 of 18 items leaves exactly 7 behind, so choosing 11 and choosing which 7 to leave out are the same count: 18 choose 11 = 18 choose 7 = 31,824. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(18, 11) = 1,270,312,243,200. Each of the 31,824 combinations can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also