20 Choose 0

Combination Calculator
Total items (n)
Items chosen (k)

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
k20 choose k
01
120
2190
31,140
44,845
515,504
638,760
777,520
8125,970
9167,960
10184,756
11167,960
12125,970
1377,520
1438,760
1515,504
164,845
171,140
18190
1920
201

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

See Also

Recalculate with different values ↑

n choose 0 for other n

n choose 0Answer
6 choose 01
7 choose 01
8 choose 01
9 choose 01
10 choose 01
11 choose 01
12 choose 01
13 choose 01
14 choose 01
15 choose 01
16 choose 01
17 choose 01
18 choose 01
19 choose 01
20 choose 01

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