12 Choose 0

Combination Calculator

What is 12 choose 0?

Answer

12 choose 0 is

Order doesn't matter, no repeats: 1 way to choose 0 of 12 items.

There is exactly one way: take none.

C(12, 0) = 12! / (0! · 12!)

= 1

0! = 1 (an empty product), so 12! cancels out completely.

Row 12 of Pascal's triangle
k	12 choose k
0	1
1	12
2	66
3	220
4	495
5	792
6	924
7	792
8	495
9	220
10	66
11	12
12	1

Row sum: 2¹² = 4,096 — all subsets of 12 items.

n choose 0 for other n

n choose 0	Answer
5 choose 0	1
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

FAQ

What is 12 choose 0?

12 choose 0 is 1

Why is 12 choose 0 the same as 12 choose 12?

Every way to choose 0 of 12 items leaves exactly 12 behind, so choosing 0 and choosing which 12 to leave out are the same count: 12 choose 0 = 12 choose 12 = 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(12, 0) = 12 choose 0 = 1. Order starts to matter from 2 items on: n × (n − 1) arrangements.

12 Choose 0

What is 12 choose 0?

See Also

n choose 0 for other n

FAQ

What is 12 choose 0?

Why is 12 choose 0 the same as 12 choose 12?

How many ways are there if order matters?

See Also