20 Choose 19

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

What is 20 choose 19?

Answer

20 choose 19 is
20

Order doesn't matter, no repeats: 20 ways to choose 19 of 20 items.

Choosing 19 of 20 is the same as leaving 1 out: C(20, 19) = C(20, 1).

C(20, 19) = 20! / (19! · 1!)

= C(20, 1)

= 20 / 1

= 20

If order matters (permutations): P(20, 19) = 20 × 19 × 18 × … × 2 = 2,432,902,008,176,640,000 — each combination in 19! = 121,645,100,408,832,000 orders.

Row 20 of Pascal's triangle
k20 choose k
01
120
2190
31,140
44,845
515,504
638,760
777,520
8125,970
9167,960
10184,756
11167,960
12125,970
1377,520
1438,760
1515,504
164,845
171,140
18190
1920
201

Row sum: 220 = 1,048,576 — all subsets of 20 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 20 choose 19?

20 choose 19 is 20

Why is 20 choose 19 the same as 20 choose 1?

Every way to choose 19 of 20 items leaves exactly 1 behind, so choosing 19 and choosing which one to leave out are the same count: 20 choose 19 = 20 choose 1 = 20. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(20, 19) = 2,432,902,008,176,640,000. Each of the 20 combinations 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