18 Choose 1

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

What is 18 choose 1?

Answer

18 choose 1 is
18

Order doesn't matter, no repeats: 18 ways to choose 1 of 18 items.

C(18, 1) = 18! / (1! · 17!)

= 18 / 1

= 18

Row 18 of Pascal's triangle
k18 choose k
01
118
2153
3816
43,060
58,568
618,564
731,824
843,758
948,620
1043,758
1131,824
1218,564
138,568
143,060
15816
16153
1718
181

Row sum: 218 = 262,144 — all subsets of 18 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 18 choose 1?

18 choose 1 is 18

Why is 18 choose 1 the same as 18 choose 17?

Every way to choose 1 of 18 items leaves exactly 17 behind, so choosing 1 and choosing which 17 to leave out are the same count: 18 choose 1 = 18 choose 17 = 18. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

The same 18: with 1 chosen item there is only one order, so P(18, 1) = 18 choose 1 = 18. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also