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7 Choose 3

Combination Calculator

What is 7 choose 3?

Answer

7 choose 3 is

35

Order doesn't matter, no repeats: 35 ways to choose 3 of 7 items.

C(7, 3) = 7! / (3! · 4!)

= 35

If order matters (permutations): P(7, 3) = 7 × 6 × 5 = 210 — each combination in 3! = 6 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--3

<a href="https://calculat.io/en/number/combinations/7--3">7 Choose 3: Combinations C(7, 3) - Calculatio</a>

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7 Choose 3: Combinations C(7, 3). 7 choose 3 = 35: the number of ways to choose 3 of 7 items when order doesn't matter and nothing repeats. C(7, 3) = (7 × 6 × 5) / (3 × 2 × 1).

https://calculat.io/en/number/combinations/7--3/generated.jpg

n choose 3 for other n

n choose 3	Answer
1 choose 3	0
2 choose 3	0
3 choose 3	1
4 choose 3	4
5 choose 3	10
6 choose 3	20
7 choose 3	35
8 choose 3	56
9 choose 3	84
10 choose 3	120
11 choose 3	165
12 choose 3	220
13 choose 3	286
14 choose 3	364
15 choose 3	455

Recalculate with different values ↑

FAQ

What is 7 choose 3?

7 choose 3 is 35

Why is 7 choose 3 the same as 7 choose 4?

Every way to choose 3 of 7 items leaves exactly 4 behind, so choosing 3 and choosing which 4 to leave out are the same count: 7 choose 3 = 7 choose 4 = 35. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(7, 3) = 210. Each of the 35 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.