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19 Choose 2

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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!)

= 171

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

Row 19 of Pascal's triangle
k	19 choose k
0	1
1	19
2	171
3	969
4	3,876
5	11,628
6	27,132
7	50,388
8	75,582
9	92,378
10	92,378
11	75,582
12	50,388
13	27,132
14	11,628
15	3,876
16	969
17	171
18	19
19	1

Row sum: 2¹⁹ = 524,288 — all subsets of 19 items.

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https://calculat.io/en/number/combinations/19--2

<a href="https://calculat.io/en/number/combinations/19--2">19 Choose 2: Combinations C(19, 2) - Calculatio</a>

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19 Choose 2: Combinations C(19, 2). 19 choose 2 = 171: the number of ways to choose 2 of 19 items when order doesn't matter and nothing repeats. C(19, 2) = (19 × 18) / (2 × 1).

https://calculat.io/en/number/combinations/19--2/generated.jpg

n choose 2 for other n

n choose 2	Answer
6 choose 2	15
7 choose 2	21
8 choose 2	28
9 choose 2	36
10 choose 2	45
11 choose 2	55
12 choose 2	66
13 choose 2	78
14 choose 2	91
15 choose 2	105
16 choose 2	120
17 choose 2	136
18 choose 2	153
19 choose 2	171
20 choose 2	190

Recalculate with different values ↑

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