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17 Choose 2

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What is 17 choose 2?

Answer

17 choose 2 is

136

Order doesn't matter, no repeats: 136 ways to choose 2 of 17 items.

C(17, 2) = 17! / (2! · 15!)

= 136

If order matters (permutations): P(17, 2) = 17 × 16 = 272 — each combination in 2! = 2 orders.

Row 17 of Pascal's triangle
k	17 choose k
0	1
1	17
2	136
3	680
4	2,380
5	6,188
6	12,376
7	19,448
8	24,310
9	24,310
10	19,448
11	12,376
12	6,188
13	2,380
14	680
15	136
16	17
17	1

Row sum: 2¹⁷ = 131,072 — all subsets of 17 items.

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See Also

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https://calculat.io/en/number/combinations/17--2

<a href="https://calculat.io/en/number/combinations/17--2">17 Choose 2: Combinations C(17, 2) - Calculatio</a>

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17 Choose 2: Combinations C(17, 2). 17 choose 2 = 136: the number of ways to choose 2 of 17 items when order doesn't matter and nothing repeats. C(17, 2) = (17 × 16) / (2 × 1).

https://calculat.io/en/number/combinations/17--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 17 choose 2?

17 choose 2 is 136

Why is 17 choose 2 the same as 17 choose 15?

Every way to choose 2 of 17 items leaves exactly 15 behind, so choosing 2 and choosing which 15 to leave out are the same count: 17 choose 2 = 17 choose 15 = 136. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(17, 2) = 272. Each of the 136 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also