18 Choose 3

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

What is 18 choose 3?

Answer

18 choose 3 is
816

Order doesn't matter, no repeats: 816 ways to choose 3 of 18 items.

C(18, 3) = 18! / (3! · 15!)

= (18 × 17 × 16) / (3 × 2 × 1)
= 4,896 / 6

= 816

If order matters (permutations): P(18, 3) = 18 × 17 × 16 = 4,896 — each combination in 3! = 6 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 3 for other n

n choose 3Answer
9 choose 384
10 choose 3120
11 choose 3165
12 choose 3220
13 choose 3286
14 choose 3364
15 choose 3455
16 choose 3560
17 choose 3680
18 choose 3816
19 choose 3969
20 choose 31,140
25 choose 32,300
40 choose 39,880
100 choose 3161,700

FAQ

What is 18 choose 3?

18 choose 3 is 816

Why is 18 choose 3 the same as 18 choose 15?

Every way to choose 3 of 18 items leaves exactly 15 behind, so choosing 3 and choosing which 15 to leave out are the same count: 18 choose 3 = 18 choose 15 = 816. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(18, 3) = 4,896. Each of the 816 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also