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11 Choose 9

Combination Calculator

What is 11 choose 9?

Answer

11 choose 9 is

55

Order doesn't matter, no repeats: 55 ways to choose 9 of 11 items.

Choosing 9 of 11 is the same as leaving 2 out: C(11, 9) = C(11, 2).

C(11, 9) = 11! / (9! · 2!)

= C(11, 2)

= 55

If order matters (permutations): P(11, 9) = 11 × 10 × 9 × … × 3 = 19,958,400 — each combination in 9! = 362,880 orders.

Row 11 of Pascal's triangle
k	11 choose k
0	1
1	11
2	55
3	165
4	330
5	462
6	462
7	330
8	165
9	55
10	11
11	1

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

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https://calculat.io/en/number/combinations/11--9

<a href="https://calculat.io/en/number/combinations/11--9">11 Choose 9: Combinations C(11, 9) - Calculatio</a>

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11 Choose 9: Combinations C(11, 9). 11 choose 9 = 55: the number of ways to choose 9 of 11 items when order doesn't matter and nothing repeats. C(11, 9) = (11 × 10) / (2 × 1).

https://calculat.io/en/number/combinations/11--9/generated.jpg

n choose 9 for other n

n choose 9	Answer
9 choose 9	1
10 choose 9	10
11 choose 9	55
12 choose 9	220
13 choose 9	715
14 choose 9	2,002
15 choose 9	5,005
16 choose 9	11,440
17 choose 9	24,310
18 choose 9	48,620
19 choose 9	92,378
20 choose 9	167,960

Recalculate with different values ↑

FAQ

What is 11 choose 9?

11 choose 9 is 55

Why is 11 choose 9 the same as 11 choose 2?

Every way to choose 9 of 11 items leaves exactly 2 behind, so choosing 9 and choosing which 2 to leave out are the same count: 11 choose 9 = 11 choose 2 = 55. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(11, 9) = 19,958,400. Each of the 55 combinations can be put in order in 9! = 362,880 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.