7 Choose 2

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

What is 7 choose 2?

Answer

7 choose 2 is
21

Order doesn't matter, no repeats: 21 ways to choose 2 of 7 items.

C(7, 2) = 7! / (2! · 5!)

= (7 × 6) / (2 × 1)
= 42 / 2

= 21

If order matters (permutations): P(7, 2) = 7 × 6 = 42 — each combination in 2! = 2 orders.

Row 7 of Pascal's triangle
k7 choose k
01
17
221
335
435
521
67
71

Row sum: 27 = 128 — all subsets of 7 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 7 choose 2?

7 choose 2 is 21

Why is 7 choose 2 the same as 7 choose 5?

Every way to choose 2 of 7 items leaves exactly 5 behind, so choosing 2 and choosing which 5 to leave out are the same count: 7 choose 2 = 7 choose 5 = 21. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(7, 2) = 42. Each of the 21 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also