20 Choose 1

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

What is 20 choose 1?

Answer

20 choose 1 is
20

Order doesn't matter, no repeats: 20 ways to choose 1 of 20 items.

C(20, 1) = 20! / (1! · 19!)

= 20 / 1

= 20

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 1 for other n

n choose 1Answer
6 choose 16
7 choose 17
8 choose 18
9 choose 19
10 choose 110
11 choose 111
12 choose 112
13 choose 113
14 choose 114
15 choose 115
16 choose 116
17 choose 117
18 choose 118
19 choose 119
20 choose 120

FAQ

What is 20 choose 1?

20 choose 1 is 20

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

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

How many ways are there if order matters?

The same 20: with 1 chosen item there is only one order, so P(20, 1) = 20 choose 1 = 20. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also