13 Choose 11

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

What is 13 choose 11?

Answer

13 choose 11 is
78

Order doesn't matter, no repeats: 78 ways to choose 11 of 13 items.

Choosing 11 of 13 is the same as leaving 2 out: C(13, 11) = C(13, 2).

C(13, 11) = 13! / (11! · 2!)

= C(13, 2)

= (13 × 12) / (2 × 1)
= 156 / 2

= 78

If order matters (permutations): P(13, 11) = 13 × 12 × 11 × … × 3 = 3,113,510,400 — each combination in 11! = 39,916,800 orders.

Row 13 of Pascal's triangle
k13 choose k
01
113
278
3286
4715
51,287
61,716
71,716
81,287
9715
10286
1178
1213
131

Row sum: 213 = 8,192 — all subsets of 13 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 13 choose 11?

13 choose 11 is 78

Why is 13 choose 11 the same as 13 choose 2?

Every way to choose 11 of 13 items leaves exactly 2 behind, so choosing 11 and choosing which 2 to leave out are the same count: 13 choose 11 = 13 choose 2 = 78. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(13, 11) = 3,113,510,400. Each of the 78 combinations can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also