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20 Choose 0

Combination Calculator

What is 20 choose 0?

Answer

20 choose 0 is

1

Order doesn't matter, no repeats: 1 way to choose 0 of 20 items.

There is exactly one way: take none.

C(20, 0) = 20! / (0! · 20!)

= 1

0! = 1 (an empty product), so 20! cancels out completely.

Row 20 of Pascal's triangle
k	20 choose k
0	1
1	20
2	190
3	1,140
4	4,845
5	15,504
6	38,760
7	77,520
8	125,970
9	167,960
10	184,756
11	167,960
12	125,970
13	77,520
14	38,760
15	15,504
16	4,845
17	1,140
18	190
19	20
20	1

Row sum: 2²⁰ = 1,048,576 — all subsets of 20 items.

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See Also

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https://calculat.io/en/number/combinations/20--0

<a href="https://calculat.io/en/number/combinations/20--0">20 Choose 0: Combinations C(20, 0) - Calculatio</a>

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20 Choose 0: Combinations C(20, 0). 20 choose 0 = 1: the number of ways to choose 0 of 20 items when order doesn't matter and nothing repeats.

https://calculat.io/en/number/combinations/20--0/generated.jpg

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 20 choose 0?

20 choose 0 is 1

Why is 20 choose 0 the same as 20 choose 20?

Every way to choose 0 of 20 items leaves exactly 20 behind, so choosing 0 and choosing which 20 to leave out are the same count: 20 choose 0 = 20 choose 20 = 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(20, 0) = 20 choose 0 = 1. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also