5 Choose 2

Combination Calculator

What is 5 choose 2?

Answer

5 choose 2 is

Order doesn't matter, no repeats: 10 ways to choose 2 of 5 items.

C(5, 2) = 5! / (2! · 3!)

= 10

If order matters (permutations): P(5, 2) = 5 × 4 = 20 — each combination in 2! = 2 orders.

Row 5 of Pascal's triangle
k	5 choose k
0	1
1	5
2	10
3	10
4	5
5	1

Row sum: 2⁵ = 32 — all subsets of 5 items.

Found an error in the calculation or the information?

n choose 2 for other n

n choose 2	Answer
1 choose 2	0
2 choose 2	1
3 choose 2	3
4 choose 2	6
5 choose 2	10
6 choose 2	15
7 choose 2	21
8 choose 2	28
9 choose 2	36
10 choose 2	45
11 choose 2	55
12 choose 2	66
13 choose 2	78
14 choose 2	91
15 choose 2	105

Recalculate with different values ↑

FAQ

What is 5 choose 2?

5 choose 2 is 10

Why is 5 choose 2 the same as 5 choose 3?

Every way to choose 2 of 5 items leaves exactly 3 behind, so choosing 2 and choosing which 3 to leave out are the same count: 5 choose 2 = 5 choose 3 = 10. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(5, 2) = 20. Each of the 10 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

5 Choose 2

What is 5 choose 2?

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n choose 2 for other n

FAQ

What is 5 choose 2?

Why is 5 choose 2 the same as 5 choose 3?

How many ways are there if order matters?

See Also