16 Choose 2

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

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!)

= (16 × 15) / (2 × 1)
= 240 / 2

= 120

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

Row 16 of Pascal's triangle
k16 choose k
01
116
2120
3560
41,820
54,368
68,008
711,440
812,870
911,440
108,008
114,368
121,820
13560
14120
1516
161

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

See Also