19 Choose 5

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

What is 19 choose 5?

Answer

19 choose 5 is
11,628

Order doesn't matter, no repeats: 11,628 ways to choose 5 of 19 items.

C(19, 5) = 19! / (5! · 14!)

= (19 × 18 × 17 × 16 × 15) / (5 × 4 × 3 × 2 × 1)
= 1,395,360 / 120

= 11,628

If order matters (permutations): P(19, 5) = 19 × 18 × 17 × 16 × 15 = 1,395,360 — each combination in 5! = 120 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 5 for other n

n choose 5Answer
6 choose 56
7 choose 521
8 choose 556
9 choose 5126
10 choose 5252
11 choose 5462
12 choose 5792
13 choose 51,287
14 choose 52,002
15 choose 53,003
16 choose 54,368
17 choose 56,188
18 choose 58,568
19 choose 511,628
20 choose 515,504

FAQ

What is 19 choose 5?

19 choose 5 is 11,628

Why is 19 choose 5 the same as 19 choose 14?

Every way to choose 5 of 19 items leaves exactly 14 behind, so choosing 5 and choosing which 14 to leave out are the same count: 19 choose 5 = 19 choose 14 = 11,628. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 5) = 1,395,360. Each of the 11,628 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also