19 Choose 11

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

What is 19 choose 11?

Answer

19 choose 11 is
75,582

Order doesn't matter, no repeats: 75,582 ways to choose 11 of 19 items.

Choosing 11 of 19 is the same as leaving 8 out: C(19, 11) = C(19, 8).

C(19, 11) = 19! / (11! · 8!)

= C(19, 8)

= (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, 11) = 19 × 18 × 17 × … × 9 = 3,016,991,577,600 — each combination in 11! = 39,916,800 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 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 19 choose 11?

19 choose 11 is 75,582

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

Every way to choose 11 of 19 items leaves exactly 8 behind, so choosing 11 and choosing which 8 to leave out are the same count: 19 choose 11 = 19 choose 8 = 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, 11) = 3,016,991,577,600. Each of the 75,582 combinations can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also