17 Choose 1

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

What is 17 choose 1?

Answer

17 choose 1 is
17

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

C(17, 1) = 17! / (1! · 16!)

= 17 / 1

= 17

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 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 17 choose 1?

17 choose 1 is 17

Why is 17 choose 1 the same as 17 choose 16?

Every way to choose 1 of 17 items leaves exactly 16 behind, so choosing 1 and choosing which 16 to leave out are the same count: 17 choose 1 = 17 choose 16 = 17. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

The same 17: with 1 chosen item there is only one order, so P(17, 1) = 17 choose 1 = 17. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also