11 Choose 0

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

What is 11 choose 0?

Answer

11 choose 0 is
1

Order doesn't matter, no repeats: 1 way to choose 0 of 11 items.

There is exactly one way: take none.

C(11, 0) = 11! / (0! · 11!)

= 1

0! = 1 (an empty product), so 11! cancels out completely.

Row 11 of Pascal's triangle
k11 choose k
01
111
255
3165
4330
5462
6462
7330
8165
955
1011
111

Row sum: 211 = 2,048 — all subsets of 11 items.

See Also

Recalculate with different values ↑

n choose 0 for other n

n choose 0Answer
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
16 choose 01
17 choose 01
18 choose 01

FAQ

What is 11 choose 0?

11 choose 0 is 1

Why is 11 choose 0 the same as 11 choose 11?

Every way to choose 0 of 11 items leaves exactly 11 behind, so choosing 0 and choosing which 11 to leave out are the same count: 11 choose 0 = 11 choose 11 = 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(11, 0) = 11 choose 0 = 1. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also