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13 Choose 2

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What is 13 choose 2?

Answer

13 choose 2 is

78

Order doesn't matter, no repeats: 78 ways to choose 2 of 13 items.

C(13, 2) = 13! / (2! · 11!)

= 78

If order matters (permutations): P(13, 2) = 13 × 12 = 156 — each combination in 2! = 2 orders.

Row 13 of Pascal's triangle
k	13 choose k
0	1
1	13
2	78
3	286
4	715
5	1,287
6	1,716
7	1,716
8	1,287
9	715
10	286
11	78
12	13
13	1

Row sum: 2¹³ = 8,192 — all subsets of 13 items.

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https://calculat.io/en/number/combinations/13--2

<a href="https://calculat.io/en/number/combinations/13--2">13 Choose 2: Combinations C(13, 2) - Calculatio</a>

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13 Choose 2: Combinations C(13, 2). 13 choose 2 = 78: the number of ways to choose 2 of 13 items when order doesn't matter and nothing repeats. C(13, 2) = (13 × 12) / (2 × 1).

https://calculat.io/en/number/combinations/13--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 13 choose 2?

13 choose 2 is 78

Why is 13 choose 2 the same as 13 choose 11?

Every way to choose 2 of 13 items leaves exactly 11 behind, so choosing 2 and choosing which 11 to leave out are the same count: 13 choose 2 = 13 choose 11 = 78. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(13, 2) = 156. Each of the 78 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.