19 Choose 19

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What is 19 choose 19?

Answer

19 choose 19 is

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
k	19 choose k
0	1
1	19
2	171
3	969
4	3,876
5	11,628
6	27,132
7	50,388
8	75,582
9	92,378
10	92,378
11	75,582
12	50,388
13	27,132
14	11,628
15	3,876
16	969
17	171
18	19
19	1

Row sum: 2¹⁹ = 524,288 — all subsets of 19 items.

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n choose 19 for other n

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

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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)!.

19 Choose 19

What is 19 choose 19?

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n choose 19 for other n

FAQ

What is 19 choose 19?

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

How many ways are there if order matters?

See Also