13 Choose 0

Combination Calculator

What is 13 choose 0?

Answer

13 choose 0 is

Order doesn't matter, no repeats: 1 way to choose 0 of 13 items.

There is exactly one way: take none.

C(13, 0) = 13! / (0! · 13!)

= 1

0! = 1 (an empty product), so 13! cancels out completely.

Row 13 of Pascal's triangle
k	13 choose k
0	1
1	13
2	78
3	286
4	715
5	1,287
6	1,716
7	1,716
8	1,287
9	715
10	286
11	78
12	13
13	1

Row sum: 2¹³ = 8,192 — all subsets of 13 items.

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

FAQ

What is 13 choose 0?

13 choose 0 is 1

Why is 13 choose 0 the same as 13 choose 13?

Every way to choose 0 of 13 items leaves exactly 13 behind, so choosing 0 and choosing which 13 to leave out are the same count: 13 choose 0 = 13 choose 13 = 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(13, 0) = 13 choose 0 = 1. Order starts to matter from 2 items on: n × (n − 1) arrangements.

13 Choose 0

What is 13 choose 0?

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n choose 0 for other n

FAQ

What is 13 choose 0?

Why is 13 choose 0 the same as 13 choose 13?

How many ways are there if order matters?

See Also