8 Choose 1

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

What is 8 choose 1?

Answer

8 choose 1 is
8

Order doesn't matter, no repeats: 8 ways to choose 1 of 8 items.

C(8, 1) = 8! / (1! · 7!)

= 8 / 1

= 8

Row 8 of Pascal's triangle
k8 choose k
01
18
228
356
470
556
628
78
81

Row sum: 28 = 256 — all subsets of 8 items.

See Also

Recalculate with different values ↑

n choose 1 for other n

n choose 1Answer
1 choose 11
2 choose 12
3 choose 13
4 choose 14
5 choose 15
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

FAQ

What is 8 choose 1?

8 choose 1 is 8

Why is 8 choose 1 the same as 8 choose 7?

Every way to choose 1 of 8 items leaves exactly 7 behind, so choosing 1 and choosing which 7 to leave out are the same count: 8 choose 1 = 8 choose 7 = 8. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

The same 8: with 1 chosen item there is only one order, so P(8, 1) = 8 choose 1 = 8. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also