9 Choose 1

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

What is 9 choose 1?

Answer

9 choose 1 is
9

Order doesn't matter, no repeats: 9 ways to choose 1 of 9 items.

C(9, 1) = 9! / (1! · 8!)

= 9 / 1

= 9

Row 9 of Pascal's triangle
k9 choose k
01
19
236
384
4126
5126
684
736
89
91

Row sum: 29 = 512 — all subsets of 9 items.

See Also

FAQ

What is 9 choose 1?

9 choose 1 is 9

Why is 9 choose 1 the same as 9 choose 8?

Every way to choose 1 of 9 items leaves exactly 8 behind, so choosing 1 and choosing which 8 to leave out are the same count: 9 choose 1 = 9 choose 8 = 9. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

The same 9: with 1 chosen item there is only one order, so P(9, 1) = 9 choose 1 = 9. Order starts to matter from 2 items on: n × (n − 1) arrangements.