19 Choose 13

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

What is 19 choose 13?

Answer

19 choose 13 is
27,132

Order doesn't matter, no repeats: 27,132 ways to choose 13 of 19 items.

Choosing 13 of 19 is the same as leaving 6 out: C(19, 13) = C(19, 6).

C(19, 13) = 19! / (13! · 6!)

= C(19, 6)

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

= 27,132

If order matters (permutations): P(19, 13) = 19 × 18 × 17 × … × 7 = 168,951,528,345,600 — each combination in 13! = 6,227,020,800 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 13 for other n

n choose 13Answer
13 choose 131
14 choose 1314
15 choose 13105
16 choose 13560
17 choose 132,380
18 choose 138,568
19 choose 1327,132
20 choose 1377,520

FAQ

What is 19 choose 13?

19 choose 13 is 27,132

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

Every way to choose 13 of 19 items leaves exactly 6 behind, so choosing 13 and choosing which 6 to leave out are the same count: 19 choose 13 = 19 choose 6 = 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, 13) = 168,951,528,345,600. Each of the 27,132 combinations can be put in order in 13! = 6,227,020,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also