3 Choose 1

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

What is 3 choose 1?

Answer

3 choose 1 is
3

Order doesn't matter, no repeats: 3 ways to choose 1 of 3 items.

C(3, 1) = 3! / (1! · 2!)

= 3 / 1

= 3

Row 3 of Pascal's triangle
k3 choose k
01
13
23
31

Row sum: 23 = 8 — all subsets of 3 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 3 choose 1?

3 choose 1 is 3

Why is 3 choose 1 the same as 3 choose 2?

Every way to choose 1 of 3 items leaves exactly 2 behind, so choosing 1 and choosing which 2 to leave out are the same count: 3 choose 1 = 3 choose 2 = 3. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

The same 3: with 1 chosen item there is only one order, so P(3, 1) = 3 choose 1 = 3. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also