15 Choose 11

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

What is 15 choose 11?

Answer

15 choose 11 is
1,365

Order doesn't matter, no repeats: 1,365 ways to choose 11 of 15 items.

Choosing 11 of 15 is the same as leaving 4 out: C(15, 11) = C(15, 4).

C(15, 11) = 15! / (11! · 4!)

= C(15, 4)

= (15 × 14 × 13 × 12) / (4 × 3 × 2 × 1)
= 32,760 / 24

= 1,365

If order matters (permutations): P(15, 11) = 15 × 14 × 13 × … × 5 = 54,486,432,000 — each combination in 11! = 39,916,800 orders.

Row 15 of Pascal's triangle
k15 choose k
01
115
2105
3455
41,365
53,003
65,005
76,435
86,435
95,005
103,003
111,365
12455
13105
1415
151

Row sum: 215 = 32,768 — all subsets of 15 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 15 choose 11?

15 choose 11 is 1,365

Why is 15 choose 11 the same as 15 choose 4?

Every way to choose 11 of 15 items leaves exactly 4 behind, so choosing 11 and choosing which 4 to leave out are the same count: 15 choose 11 = 15 choose 4 = 1,365. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(15, 11) = 54,486,432,000. Each of the 1,365 combinations can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also