11 Choose 9

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

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)

= (11 × 10) / (2 × 1)
= 110 / 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
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 9 for other n

n choose 9Answer
9 choose 91
10 choose 910
11 choose 955
12 choose 9220
13 choose 9715
14 choose 92,002
15 choose 95,005
16 choose 911,440
17 choose 924,310
18 choose 948,620
19 choose 992,378
20 choose 9167,960

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)!.

See Also