19 Choose 6

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

What is 19 choose 6?

Answer

19 choose 6 is
27,132

Order doesn't matter, no repeats: 27,132 ways to choose 6 of 19 items.

C(19, 6) = 19! / (6! · 13!)

= (19 × 18 × 17 × 16 × 15 × 14) / (6 × 5 × 4 × 3 × 2 × 1)
= 19,535,040 / 720

= 27,132

If order matters (permutations): P(19, 6) = 19 × 18 × 17 × 16 × 15 × 14 = 19,535,040 — each combination in 6! = 720 orders.

Row 19 of Pascal's triangle
k19 choose k
01
119
2171
3969
43,876
511,628
627,132
750,388
875,582
992,378
1092,378
1175,582
1250,388
1327,132
1411,628
153,876
16969
17171
1819
191

Row sum: 219 = 524,288 — all subsets of 19 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 19 choose 6?

19 choose 6 is 27,132

Why is 19 choose 6 the same as 19 choose 13?

Every way to choose 6 of 19 items leaves exactly 13 behind, so choosing 6 and choosing which 13 to leave out are the same count: 19 choose 6 = 19 choose 13 = 27,132. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 6) = 19,535,040. Each of the 27,132 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also