18 Choose 8

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

What is 18 choose 8?

Answer

18 choose 8 is
43,758

Order doesn't matter, no repeats: 43,758 ways to choose 8 of 18 items.

C(18, 8) = 18! / (8! · 10!)

= (18 × 17 × 16 × … × 11) / (8 × 7 × 6 × … × 1)

8 factors on top and bottom

= 1,764,322,560 / 40,320

= 43,758

If order matters (permutations): P(18, 8) = 18 × 17 × 16 × … × 11 = 1,764,322,560 — each combination in 8! = 40,320 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 8 for other n

n choose 8Answer
8 choose 81
9 choose 89
10 choose 845
11 choose 8165
12 choose 8495
13 choose 81,287
14 choose 83,003
15 choose 86,435
16 choose 812,870
17 choose 824,310
18 choose 843,758
19 choose 875,582
20 choose 8125,970

FAQ

What is 18 choose 8?

18 choose 8 is 43,758

Why is 18 choose 8 the same as 18 choose 10?

Every way to choose 8 of 18 items leaves exactly 10 behind, so choosing 8 and choosing which 10 to leave out are the same count: 18 choose 8 = 18 choose 10 = 43,758. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(18, 8) = 1,764,322,560. Each of the 43,758 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also