19 Choose 19

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

What is 19 choose 19?

Answer

19 choose 19 is
1

Order doesn't matter, no repeats: 1 way to choose 19 of 19 items.

There is exactly one way: take all.

C(19, 19) = 19! / (19! · 0!)

= 1

0! = 1 (an empty product), so 19! cancels out completely.

If order matters (permutations): P(19, 19) = 19 × 18 × 17 × … × 1 = 121,645,100,408,832,000 — each combination in 19! = 121,645,100,408,832,000 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 19 for other n

n choose 19Answer
19 choose 191
20 choose 1920

FAQ

What is 19 choose 19?

19 choose 19 is 1

Why is 19 choose 19 the same as 19 choose 0?

Every way to choose 19 of 19 items leaves exactly 0 behind, so choosing 19 and choosing which 0 to leave out are the same count: 19 choose 19 = 19 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 19) = 121,645,100,408,832,000. The only combination — all 19 items — can be put in order in 19! = 121,645,100,408,832,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also