5 Choose 2

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

What is 5 choose 2?

Answer

5 choose 2 is
10

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

C(5, 2) = 5! / (2! · 3!)

= (5 × 4) / (2 × 1)
= 20 / 2

= 10

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

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 2 for other n

n choose 2Answer
1 choose 20
2 choose 21
3 choose 23
4 choose 26
5 choose 210
6 choose 215
7 choose 221
8 choose 228
9 choose 236
10 choose 245
11 choose 255
12 choose 266
13 choose 278
14 choose 291
15 choose 2105

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)!.

See Also