18 Choose 2

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

What is 18 choose 2?

Answer

18 choose 2 is
153

Order doesn't matter, no repeats: 153 ways to choose 2 of 18 items.

C(18, 2) = 18! / (2! · 16!)

= (18 × 17) / (2 × 1)
= 306 / 2

= 153

If order matters (permutations): P(18, 2) = 18 × 17 = 306 — each combination in 2! = 2 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 2 for other n

n choose 2Answer
6 choose 215
7 choose 221
8 choose 228
9 choose 236
10 choose 245
11 choose 255
12 choose 266
13 choose 278
14 choose 291
15 choose 2105
16 choose 2120
17 choose 2136
18 choose 2153
19 choose 2171
20 choose 2190

FAQ

What is 18 choose 2?

18 choose 2 is 153

Why is 18 choose 2 the same as 18 choose 16?

Every way to choose 2 of 18 items leaves exactly 16 behind, so choosing 2 and choosing which 16 to leave out are the same count: 18 choose 2 = 18 choose 16 = 153. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(18, 2) = 306. Each of the 153 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also