19 Choose 18

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

What is 19 choose 18?

Answer

19 choose 18 is
19

Order doesn't matter, no repeats: 19 ways to choose 18 of 19 items.

Choosing 18 of 19 is the same as leaving 1 out: C(19, 18) = C(19, 1).

C(19, 18) = 19! / (18! · 1!)

= C(19, 1)

= 19 / 1

= 19

If order matters (permutations): P(19, 18) = 19 × 18 × 17 × … × 2 = 121,645,100,408,832,000 — each combination in 18! = 6,402,373,705,728,000 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 18 for other n

n choose 18Answer
18 choose 181
19 choose 1819
20 choose 18190

FAQ

What is 19 choose 18?

19 choose 18 is 19

Why is 19 choose 18 the same as 19 choose 1?

Every way to choose 18 of 19 items leaves exactly 1 behind, so choosing 18 and choosing which one to leave out are the same count: 19 choose 18 = 19 choose 1 = 19. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 18) = 121,645,100,408,832,000. Each of the 19 combinations can be put in order in 18! = 6,402,373,705,728,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also