16 Choose 0

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What is 16 choose 0?

Answer

16 choose 0 is

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
k	16 choose k
0	1
1	16
2	120
3	560
4	1,820
5	4,368
6	8,008
7	11,440
8	12,870
9	11,440
10	8,008
11	4,368
12	1,820
13	560
14	120
15	16
16	1

Row sum: 2¹⁶ = 65,536 — all subsets of 16 items.

Found an error in the calculation or the information?

n choose 0 for other n

n choose 0	Answer
6 choose 0	1
7 choose 0	1
8 choose 0	1
9 choose 0	1
10 choose 0	1
11 choose 0	1
12 choose 0	1
13 choose 0	1
14 choose 0	1
15 choose 0	1
16 choose 0	1
17 choose 0	1
18 choose 0	1
19 choose 0	1
20 choose 0	1

Recalculate with different values ↑

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.

16 Choose 0

What is 16 choose 0?

See Also

n choose 0 for other n

FAQ

What is 16 choose 0?

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

How many ways are there if order matters?

See Also