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18 Choose 0

Combination Calculator

What is 18 choose 0?

Answer

18 choose 0 is

1

Order doesn't matter, no repeats: 1 way to choose 0 of 18 items.

There is exactly one way: take none.

C(18, 0) = 18! / (0! · 18!)

= 1

0! = 1 (an empty product), so 18! cancels out completely.

Row 18 of Pascal's triangle
k	18 choose k
0	1
1	18
2	153
3	816
4	3,060
5	8,568
6	18,564
7	31,824
8	43,758
9	48,620
10	43,758
11	31,824
12	18,564
13	8,568
14	3,060
15	816
16	153
17	18
18	1

Row sum: 2¹⁸ = 262,144 — all subsets of 18 items.

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See Also

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https://calculat.io/en/number/combinations/18--0

<a href="https://calculat.io/en/number/combinations/18--0">18 Choose 0: Combinations C(18, 0) - Calculatio</a>

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18 Choose 0: Combinations C(18, 0). 18 choose 0 = 1: the number of ways to choose 0 of 18 items when order doesn't matter and nothing repeats.

https://calculat.io/en/number/combinations/18--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 18 choose 0?

18 choose 0 is 1

Why is 18 choose 0 the same as 18 choose 18?

Every way to choose 0 of 18 items leaves exactly 18 behind, so choosing 0 and choosing which 18 to leave out are the same count: 18 choose 0 = 18 choose 18 = 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(18, 0) = 18 choose 0 = 1. Order starts to matter from 2 items on: n × (n − 1) arrangements.