16 Choose 0

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

What is 16 choose 0?

Answer

16 choose 0 is
1

Order doesn't matter, no repeats: 1 way to choose 0 of 16 items.

There is exactly one way: take none.

C(16, 0) = 16! / (0! · 16!)

= 1

0! = 1 (an empty product), so 16! cancels out completely.

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 0 for other n

n choose 0Answer
6 choose 01
7 choose 01
8 choose 01
9 choose 01
10 choose 01
11 choose 01
12 choose 01
13 choose 01
14 choose 01
15 choose 01
16 choose 01
17 choose 01
18 choose 01
19 choose 01
20 choose 01

FAQ

What is 16 choose 0?

16 choose 0 is 1

Why is 16 choose 0 the same as 16 choose 16?

Every way to choose 0 of 16 items leaves exactly 16 behind, so choosing 0 and choosing which 16 to leave out are the same count: 16 choose 0 = 16 choose 16 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

The same 1: with 0 chosen items there is only one order, so P(16, 0) = 16 choose 0 = 1. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also