15 Choose 0

Combination Calculator

What is 15 choose 0?

Answer

15 choose 0 is

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
k	15 choose k
0	1
1	15
2	105
3	455
4	1,365
5	3,003
6	5,005
7	6,435
8	6,435
9	5,005
10	3,003
11	1,365
12	455
13	105
14	15
15	1

Row sum: 2¹⁵ = 32,768 — all subsets of 15 items.

Found an error in the calculation or the information?

n choose 0 for other n

n choose 0	Answer
6 choose 0	1
7 choose 0	1
8 choose 0	1
9 choose 0	1
10 choose 0	1
11 choose 0	1
12 choose 0	1
13 choose 0	1
14 choose 0	1
15 choose 0	1
16 choose 0	1
17 choose 0	1
18 choose 0	1
19 choose 0	1
20 choose 0	1

Recalculate with different values ↑

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.

15 Choose 0

What is 15 choose 0?

See Also

n choose 0 for other n

FAQ

What is 15 choose 0?

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

How many ways are there if order matters?

See Also