17 Choose 0

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Total items (n)
Items chosen (k)

What is 17 choose 0?

Answer

17 choose 0 is
1

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
k17 choose k
01
117
2136
3680
42,380
56,188
612,376
719,448
824,310
924,310
1019,448
1112,376
126,188
132,380
14680
15136
1617
171

Row sum: 217 = 131,072 — all subsets of 17 items.

See Also

Recalculate with different values ↑

n choose 0 for other n

n choose 0Answer
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16 choose 01
17 choose 01
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19 choose 01
20 choose 01

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.

See Also