19 Choose 0

Combination Calculator

What is 19 choose 0?

Answer

19 choose 0 is

Order doesn't matter, no repeats: 1 way to choose 0 of 19 items.

There is exactly one way: take none.

C(19, 0) = 19! / (0! · 19!)

= 1

0! = 1 (an empty product), so 19! cancels out completely.

Row 19 of Pascal's triangle
k	19 choose k
0	1
1	19
2	171
3	969
4	3,876
5	11,628
6	27,132
7	50,388
8	75,582
9	92,378
10	92,378
11	75,582
12	50,388
13	27,132
14	11,628
15	3,876
16	969
17	171
18	19
19	1

Row sum: 2¹⁹ = 524,288 — all subsets of 19 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 19 choose 0?

19 choose 0 is 1

Why is 19 choose 0 the same as 19 choose 19?

Every way to choose 0 of 19 items leaves exactly 19 behind, so choosing 0 and choosing which 19 to leave out are the same count: 19 choose 0 = 19 choose 19 = 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(19, 0) = 19 choose 0 = 1. Order starts to matter from 2 items on: n × (n − 1) arrangements.

19 Choose 0

What is 19 choose 0?

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n choose 0 for other n

FAQ

What is 19 choose 0?

Why is 19 choose 0 the same as 19 choose 19?

How many ways are there if order matters?

See Also