5 Choose 1

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

What is 5 choose 1?

Answer

5 choose 1 is
5

Order doesn't matter, no repeats: 5 ways to choose 1 of 5 items.

C(5, 1) = 5! / (1! · 4!)

= 5 / 1

= 5

Row 5 of Pascal's triangle
k5 choose k
01
15
210
310
45
51

Row sum: 25 = 32 — all subsets of 5 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 5 choose 1?

5 choose 1 is 5

Why is 5 choose 1 the same as 5 choose 4?

Every way to choose 1 of 5 items leaves exactly 4 behind, so choosing 1 and choosing which 4 to leave out are the same count: 5 choose 1 = 5 choose 4 = 5. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

The same 5: with 1 chosen item there is only one order, so P(5, 1) = 5 choose 1 = 5. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also