10 Choose 0

Combination Calculator

What is 10 choose 0?

Answer

10 choose 0 is

Order doesn't matter, no repeats: 1 way to choose 0 of 10 items.

There is exactly one way: take none.

C(10, 0) = 10! / (0! · 10!)

= 1

0! = 1 (an empty product), so 10! cancels out completely.

Row 10 of Pascal's triangle
k	10 choose k
0	1
1	10
2	45
3	120
4	210
5	252
6	210
7	120
8	45
9	10
10	1

Row sum: 2¹⁰ = 1,024 — all subsets of 10 items.

Found an error in the calculation or the information?

n choose 0 for other n

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

Recalculate with different values ↑

FAQ

What is 10 choose 0?

10 choose 0 is 1

Why is 10 choose 0 the same as 10 choose 10?

Every way to choose 0 of 10 items leaves exactly 10 behind, so choosing 0 and choosing which 10 to leave out are the same count: 10 choose 0 = 10 choose 10 = 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(10, 0) = 10 choose 0 = 1. Order starts to matter from 2 items on: n × (n − 1) arrangements.

10 Choose 0

What is 10 choose 0?

See Also

n choose 0 for other n

FAQ

What is 10 choose 0?

Why is 10 choose 0 the same as 10 choose 10?

How many ways are there if order matters?

See Also