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16 Choose 2

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What is 16 choose 2?

Answer

16 choose 2 is

120

Order doesn't matter, no repeats: 120 ways to choose 2 of 16 items.

C(16, 2) = 16! / (2! · 14!)

= 120

If order matters (permutations): P(16, 2) = 16 × 15 = 240 — each combination in 2! = 2 orders.

Row 16 of Pascal's triangle
k	16 choose k
0	1
1	16
2	120
3	560
4	1,820
5	4,368
6	8,008
7	11,440
8	12,870
9	11,440
10	8,008
11	4,368
12	1,820
13	560
14	120
15	16
16	1

Row sum: 2¹⁶ = 65,536 — all subsets of 16 items.

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See Also

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https://calculat.io/en/number/combinations/16--2

<a href="https://calculat.io/en/number/combinations/16--2">16 Choose 2: Combinations C(16, 2) - Calculatio</a>

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16 Choose 2: Combinations C(16, 2). 16 choose 2 = 120: the number of ways to choose 2 of 16 items when order doesn't matter and nothing repeats. C(16, 2) = (16 × 15) / (2 × 1).

https://calculat.io/en/number/combinations/16--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 16 choose 2?

16 choose 2 is 120

Why is 16 choose 2 the same as 16 choose 14?

Every way to choose 2 of 16 items leaves exactly 14 behind, so choosing 2 and choosing which 14 to leave out are the same count: 16 choose 2 = 16 choose 14 = 120. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(16, 2) = 240. Each of the 120 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.