19 Choose 4

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

What is 19 choose 4?

Answer

19 choose 4 is
3,876

Order doesn't matter, no repeats: 3,876 ways to choose 4 of 19 items.

C(19, 4) = 19! / (4! · 15!)

= (19 × 18 × 17 × 16) / (4 × 3 × 2 × 1)
= 93,024 / 24

= 3,876

If order matters (permutations): P(19, 4) = 19 × 18 × 17 × 16 = 93,024 — each combination in 4! = 24 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 4 for other n

n choose 4Answer
7 choose 435
8 choose 470
9 choose 4126
10 choose 4210
11 choose 4330
12 choose 4495
13 choose 4715
14 choose 41,001
15 choose 41,365
16 choose 41,820
17 choose 42,380
18 choose 43,060
19 choose 43,876
20 choose 44,845
24 choose 410,626

FAQ

What is 19 choose 4?

19 choose 4 is 3,876

Why is 19 choose 4 the same as 19 choose 15?

Every way to choose 4 of 19 items leaves exactly 15 behind, so choosing 4 and choosing which 15 to leave out are the same count: 19 choose 4 = 19 choose 15 = 3,876. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 4) = 93,024. Each of the 3,876 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also