19 Choose 8

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

What is 19 choose 8?

Answer

19 choose 8 is
75,582

Order doesn't matter, no repeats: 75,582 ways to choose 8 of 19 items.

C(19, 8) = 19! / (8! · 11!)

= (19 × 18 × 17 × … × 12) / (8 × 7 × 6 × … × 1)

8 factors on top and bottom

= 3,047,466,240 / 40,320

= 75,582

If order matters (permutations): P(19, 8) = 19 × 18 × 17 × … × 12 = 3,047,466,240 — each combination in 8! = 40,320 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 8 for other n

n choose 8Answer
8 choose 81
9 choose 89
10 choose 845
11 choose 8165
12 choose 8495
13 choose 81,287
14 choose 83,003
15 choose 86,435
16 choose 812,870
17 choose 824,310
18 choose 843,758
19 choose 875,582
20 choose 8125,970

FAQ

What is 19 choose 8?

19 choose 8 is 75,582

Why is 19 choose 8 the same as 19 choose 11?

Every way to choose 8 of 19 items leaves exactly 11 behind, so choosing 8 and choosing which 11 to leave out are the same count: 19 choose 8 = 19 choose 11 = 75,582. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 8) = 3,047,466,240. Each of the 75,582 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also