15 Choose 0

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

What is 15 choose 0?

Answer

15 choose 0 is
1

Order doesn't matter, no repeats: 1 way to choose 0 of 15 items.

There is exactly one way: take none.

C(15, 0) = 15! / (0! · 15!)

= 1

0! = 1 (an empty product), so 15! cancels out completely.

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 0 for other n

n choose 0Answer
6 choose 01
7 choose 01
8 choose 01
9 choose 01
10 choose 01
11 choose 01
12 choose 01
13 choose 01
14 choose 01
15 choose 01
16 choose 01
17 choose 01
18 choose 01
19 choose 01
20 choose 01

FAQ

What is 15 choose 0?

15 choose 0 is 1

Why is 15 choose 0 the same as 15 choose 15?

Every way to choose 0 of 15 items leaves exactly 15 behind, so choosing 0 and choosing which 15 to leave out are the same count: 15 choose 0 = 15 choose 15 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

The same 1: with 0 chosen items there is only one order, so P(15, 0) = 15 choose 0 = 1. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also