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20 Choose 19

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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

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
k	20 choose k
0	1
1	20
2	190
3	1,140
4	4,845
5	15,504
6	38,760
7	77,520
8	125,970
9	167,960
10	184,756
11	167,960
12	125,970
13	77,520
14	38,760
15	15,504
16	4,845
17	1,140
18	190
19	20
20	1

Row sum: 2²⁰ = 1,048,576 — all subsets of 20 items.

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https://calculat.io/en/number/combinations/20--19

<a href="https://calculat.io/en/number/combinations/20--19">20 Choose 19: Combinations C(20, 19) - Calculatio</a>

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20 Choose 19: Combinations C(20, 19). 20 choose 19 = 20: the number of ways to choose 19 of 20 items when order doesn't matter and nothing repeats. C(20, 19) = 20 / 1.

https://calculat.io/en/number/combinations/20--19/generated.jpg

n choose 19 for other n

n choose 19	Answer
19 choose 19	1
20 choose 19	20

Recalculate with different values ↑

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