19 Choose 2

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

What is 19 choose 2?

Answer

19 choose 2 is
171

Order doesn't matter, no repeats: 171 ways to choose 2 of 19 items.

C(19, 2) = 19! / (2! · 17!)

= (19 × 18) / (2 × 1)
= 342 / 2

= 171

If order matters (permutations): P(19, 2) = 19 × 18 = 342 — each combination in 2! = 2 orders.

Row 19 of Pascal's triangle
k19 choose k
01
119
2171
3969
43,876
511,628
627,132
750,388
875,582
992,378
1092,378
1175,582
1250,388
1327,132
1411,628
153,876
16969
17171
1819
191

Row sum: 219 = 524,288 — all subsets of 19 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 19 choose 2?

19 choose 2 is 171

Why is 19 choose 2 the same as 19 choose 17?

Every way to choose 2 of 19 items leaves exactly 17 behind, so choosing 2 and choosing which 17 to leave out are the same count: 19 choose 2 = 19 choose 17 = 171. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 2) = 342. Each of the 171 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also