6 Choose 1

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

What is 6 choose 1?

Answer

6 choose 1 is
6

Order doesn't matter, no repeats: 6 ways to choose 1 of 6 items.

C(6, 1) = 6! / (1! · 5!)

= 6 / 1

= 6

Row 6 of Pascal's triangle
k6 choose k
01
16
215
320
415
56
61

Row sum: 26 = 64 — all subsets of 6 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 6 choose 1?

6 choose 1 is 6

Why is 6 choose 1 the same as 6 choose 5?

Every way to choose 1 of 6 items leaves exactly 5 behind, so choosing 1 and choosing which 5 to leave out are the same count: 6 choose 1 = 6 choose 5 = 6. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

The same 6: with 1 chosen item there is only one order, so P(6, 1) = 6 choose 1 = 6. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also