17 Choose 0

Combination Calculator

What is 17 choose 0?

Answer

17 choose 0 is

Order doesn't matter, no repeats: 1 way to choose 0 of 17 items.

There is exactly one way: take none.

C(17, 0) = 17! / (0! · 17!)

= 1

0! = 1 (an empty product), so 17! cancels out completely.

Row 17 of Pascal's triangle
k	17 choose k
0	1
1	17
2	136
3	680
4	2,380
5	6,188
6	12,376
7	19,448
8	24,310
9	24,310
10	19,448
11	12,376
12	6,188
13	2,380
14	680
15	136
16	17
17	1

Row sum: 2¹⁷ = 131,072 — all subsets of 17 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 17 choose 0?

17 choose 0 is 1

Why is 17 choose 0 the same as 17 choose 17?

Every way to choose 0 of 17 items leaves exactly 17 behind, so choosing 0 and choosing which 17 to leave out are the same count: 17 choose 0 = 17 choose 17 = 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(17, 0) = 17 choose 0 = 1. Order starts to matter from 2 items on: n × (n − 1) arrangements.

17 Choose 0

What is 17 choose 0?

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n choose 0 for other n

FAQ

What is 17 choose 0?

Why is 17 choose 0 the same as 17 choose 17?

How many ways are there if order matters?

See Also