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8 Choose 3

Combination Calculator

What is 8 choose 3?

Answer

8 choose 3 is

56

Order doesn't matter, no repeats: 56 ways to choose 3 of 8 items.

C(8, 3) = 8! / (3! · 5!)

= 56

If order matters (permutations): P(8, 3) = 8 × 7 × 6 = 336 — each combination in 3! = 6 orders.

Row 8 of Pascal's triangle
k	8 choose k
0	1
1	8
2	28
3	56
4	70
5	56
6	28
7	8
8	1

Row sum: 2⁸ = 256 — all subsets of 8 items.

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https://calculat.io/en/number/combinations/8--3

<a href="https://calculat.io/en/number/combinations/8--3">8 Choose 3: Combinations C(8, 3) - Calculatio</a>

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8 Choose 3: Combinations C(8, 3). 8 choose 3 = 56: the number of ways to choose 3 of 8 items when order doesn't matter and nothing repeats. C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1).

https://calculat.io/en/number/combinations/8--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 8 choose 3?

8 choose 3 is 56

Why is 8 choose 3 the same as 8 choose 5?

Every way to choose 3 of 8 items leaves exactly 5 behind, so choosing 3 and choosing which 5 to leave out are the same count: 8 choose 3 = 8 choose 5 = 56. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(8, 3) = 336. Each of the 56 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.