11 Choose 11

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

What is 11 choose 11?

Answer

11 choose 11 is
1

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

There is exactly one way: take all.

C(11, 11) = 11! / (11! · 0!)

= 1

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

If order matters (permutations): P(11, 11) = 11 × 10 × 9 × … × 1 = 39,916,800 — each combination in 11! = 39,916,800 orders.

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 11 for other n

n choose 11Answer
11 choose 111
12 choose 1112
13 choose 1178
14 choose 11364
15 choose 111,365
16 choose 114,368
17 choose 1112,376
18 choose 1131,824
19 choose 1175,582
20 choose 11167,960

FAQ

What is 11 choose 11?

11 choose 11 is 1

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

Every way to choose 11 of 11 items leaves exactly 0 behind, so choosing 11 and choosing which 0 to leave out are the same count: 11 choose 11 = 11 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(11, 11) = 39,916,800. The only combination — all 11 items — can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also