16 Choose 11

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

What is 16 choose 11?

Answer

16 choose 11 is
4,368

Order doesn't matter, no repeats: 4,368 ways to choose 11 of 16 items.

Choosing 11 of 16 is the same as leaving 5 out: C(16, 11) = C(16, 5).

C(16, 11) = 16! / (11! · 5!)

= C(16, 5)

= (16 × 15 × 14 × 13 × 12) / (5 × 4 × 3 × 2 × 1)
= 524,160 / 120

= 4,368

If order matters (permutations): P(16, 11) = 16 × 15 × 14 × … × 6 = 174,356,582,400 — each combination in 11! = 39,916,800 orders.

Row 16 of Pascal's triangle
k16 choose k
01
116
2120
3560
41,820
54,368
68,008
711,440
812,870
911,440
108,008
114,368
121,820
13560
14120
1516
161

Row sum: 216 = 65,536 — all subsets of 16 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 16 choose 11?

16 choose 11 is 4,368

Why is 16 choose 11 the same as 16 choose 5?

Every way to choose 11 of 16 items leaves exactly 5 behind, so choosing 11 and choosing which 5 to leave out are the same count: 16 choose 11 = 16 choose 5 = 4,368. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(16, 11) = 174,356,582,400. Each of the 4,368 combinations can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also