15 Choose 1

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

What is 15 choose 1?

Answer

15 choose 1 is
15

Order doesn't matter, no repeats: 15 ways to choose 1 of 15 items.

C(15, 1) = 15! / (1! · 14!)

= 15 / 1

= 15

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 1 for other n

n choose 1Answer
6 choose 16
7 choose 17
8 choose 18
9 choose 19
10 choose 110
11 choose 111
12 choose 112
13 choose 113
14 choose 114
15 choose 115
16 choose 116
17 choose 117
18 choose 118
19 choose 119
20 choose 120

FAQ

What is 15 choose 1?

15 choose 1 is 15

Why is 15 choose 1 the same as 15 choose 14?

Every way to choose 1 of 15 items leaves exactly 14 behind, so choosing 1 and choosing which 14 to leave out are the same count: 15 choose 1 = 15 choose 14 = 15. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

The same 15: with 1 chosen item there is only one order, so P(15, 1) = 15 choose 1 = 15. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also