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7 Choose 2

Combination Calculator

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!)

= 21

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

Row 7 of Pascal's triangle
k	7 choose k
0	1
1	7
2	21
3	35
4	35
5	21
6	7
7	1

Row sum: 2⁷ = 128 — all subsets of 7 items.

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https://calculat.io/en/number/combinations/7--2

<a href="https://calculat.io/en/number/combinations/7--2">7 Choose 2: Combinations C(7, 2) - Calculatio</a>

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7 Choose 2: Combinations C(7, 2). 7 choose 2 = 21: the number of ways to choose 2 of 7 items when order doesn't matter and nothing repeats. C(7, 2) = (7 × 6) / (2 × 1).

https://calculat.io/en/number/combinations/7--2/generated.jpg

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 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)!.