15 Choose 2

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

What is 15 choose 2?

Answer

15 choose 2 is
105

Order doesn't matter, no repeats: 105 ways to choose 2 of 15 items.

C(15, 2) = 15! / (2! · 13!)

= (15 × 14) / (2 × 1)
= 210 / 2

= 105

If order matters (permutations): P(15, 2) = 15 × 14 = 210 — each combination in 2! = 2 orders.

Row 15 of Pascal's triangle
k15 choose k
01
115
2105
3455
41,365
53,003
65,005
76,435
86,435
95,005
103,003
111,365
12455
13105
1415
151

Row sum: 215 = 32,768 — all subsets of 15 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 15 choose 2?

15 choose 2 is 105

Why is 15 choose 2 the same as 15 choose 13?

Every way to choose 2 of 15 items leaves exactly 13 behind, so choosing 2 and choosing which 13 to leave out are the same count: 15 choose 2 = 15 choose 13 = 105. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(15, 2) = 210. Each of the 105 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also