16 Choose 6

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

What is 16 choose 6?

Answer

16 choose 6 is
8,008

Order doesn't matter, no repeats: 8,008 ways to choose 6 of 16 items.

C(16, 6) = 16! / (6! · 10!)

= (16 × 15 × 14 × 13 × 12 × 11) / (6 × 5 × 4 × 3 × 2 × 1)
= 5,765,760 / 720

= 8,008

If order matters (permutations): P(16, 6) = 16 × 15 × 14 × 13 × 12 × 11 = 5,765,760 — each combination in 6! = 720 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 6 for other n

n choose 6Answer
6 choose 61
7 choose 67
8 choose 628
9 choose 684
10 choose 6210
11 choose 6462
12 choose 6924
13 choose 61,716
14 choose 63,003
15 choose 65,005
16 choose 68,008
17 choose 612,376
18 choose 618,564
19 choose 627,132
20 choose 638,760

FAQ

What is 16 choose 6?

16 choose 6 is 8,008

Why is 16 choose 6 the same as 16 choose 10?

Every way to choose 6 of 16 items leaves exactly 10 behind, so choosing 6 and choosing which 10 to leave out are the same count: 16 choose 6 = 16 choose 10 = 8,008. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(16, 6) = 5,765,760. Each of the 8,008 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also