20 Choose 2

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

What is 20 choose 2?

Answer

20 choose 2 is
190

Order doesn't matter, no repeats: 190 ways to choose 2 of 20 items.

C(20, 2) = 20! / (2! · 18!)

= (20 × 19) / (2 × 1)
= 380 / 2

= 190

If order matters (permutations): P(20, 2) = 20 × 19 = 380 — each combination in 2! = 2 orders.

Row 20 of Pascal's triangle
k20 choose k
01
120
2190
31,140
44,845
515,504
638,760
777,520
8125,970
9167,960
10184,756
11167,960
12125,970
1377,520
1438,760
1515,504
164,845
171,140
18190
1920
201

Row sum: 220 = 1,048,576 — all subsets of 20 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 20 choose 2?

20 choose 2 is 190

Why is 20 choose 2 the same as 20 choose 18?

Every way to choose 2 of 20 items leaves exactly 18 behind, so choosing 2 and choosing which 18 to leave out are the same count: 20 choose 2 = 20 choose 18 = 190. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(20, 2) = 380. Each of the 190 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also