5 Choose 0

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

What is 5 choose 0?

Answer

5 choose 0 is
1

Order doesn't matter, no repeats: 1 way to choose 0 of 5 items.

There is exactly one way: take none.

C(5, 0) = 5! / (0! · 5!)

= 1

0! = 1 (an empty product), so 5! cancels out completely.

Row 5 of Pascal's triangle
k5 choose k
01
15
210
310
45
51

Row sum: 25 = 32 — all subsets of 5 items.

See Also

Recalculate with different values ↑

n choose 0 for other n

n choose 0Answer
1 choose 01
2 choose 01
3 choose 01
4 choose 01
5 choose 01
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

FAQ

What is 5 choose 0?

5 choose 0 is 1

Why is 5 choose 0 the same as 5 choose 5?

Every way to choose 0 of 5 items leaves exactly 5 behind, so choosing 0 and choosing which 5 to leave out are the same count: 5 choose 0 = 5 choose 5 = 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(5, 0) = 5 choose 0 = 1. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also