11 Choose 3

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

What is 11 choose 3?

Answer

11 choose 3 is
165

Order doesn't matter, no repeats: 165 ways to choose 3 of 11 items.

C(11, 3) = 11! / (3! · 8!)

= (11 × 10 × 9) / (3 × 2 × 1)
= 990 / 6

= 165

If order matters (permutations): P(11, 3) = 11 × 10 × 9 = 990 — each combination in 3! = 6 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 3 for other n

n choose 3Answer
4 choose 34
5 choose 310
6 choose 320
7 choose 335
8 choose 356
9 choose 384
10 choose 3120
11 choose 3165
12 choose 3220
13 choose 3286
14 choose 3364
15 choose 3455
16 choose 3560
17 choose 3680
18 choose 3816

FAQ

What is 11 choose 3?

11 choose 3 is 165

Why is 11 choose 3 the same as 11 choose 8?

Every way to choose 3 of 11 items leaves exactly 8 behind, so choosing 3 and choosing which 8 to leave out are the same count: 11 choose 3 = 11 choose 8 = 165. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(11, 3) = 990. Each of the 165 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also