16 Choose 1

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

What is 16 choose 1?

Answer

16 choose 1 is
16

Order doesn't matter, no repeats: 16 ways to choose 1 of 16 items.

C(16, 1) = 16! / (1! · 15!)

= 16 / 1

= 16

Row 16 of Pascal's triangle
k16 choose k
01
116
2120
3560
41,820
54,368
68,008
711,440
812,870
911,440
108,008
114,368
121,820
13560
14120
1516
161

Row sum: 216 = 65,536 — all subsets of 16 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 16 choose 1?

16 choose 1 is 16

Why is 16 choose 1 the same as 16 choose 15?

Every way to choose 1 of 16 items leaves exactly 15 behind, so choosing 1 and choosing which 15 to leave out are the same count: 16 choose 1 = 16 choose 15 = 16. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

The same 16: with 1 chosen item there is only one order, so P(16, 1) = 16 choose 1 = 16. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also