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8 Choose 4

Combination Calculator

What is 8 choose 4?

Answer

8 choose 4 is

70

Order doesn't matter, no repeats: 70 ways to choose 4 of 8 items.

C(8, 4) = 8! / (4! · 4!)

= 70

If order matters (permutations): P(8, 4) = 8 × 7 × 6 × 5 = 1,680 — each combination in 4! = 24 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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See Also

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https://calculat.io/en/number/combinations/8--4

<a href="https://calculat.io/en/number/combinations/8--4">8 Choose 4: Combinations C(8, 4) - Calculatio</a>

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8 Choose 4: Combinations C(8, 4). 8 choose 4 = 70: the number of ways to choose 4 of 8 items when order doesn't matter and nothing repeats. C(8, 4) = (8 × 7 × 6 × 5) / (4 × 3 × 2 × 1).

https://calculat.io/en/number/combinations/8--4/generated.jpg

n choose 4 for other n

n choose 4	Answer
1 choose 4	0
2 choose 4	0
3 choose 4	0
4 choose 4	1
5 choose 4	5
6 choose 4	15
7 choose 4	35
8 choose 4	70
9 choose 4	126
10 choose 4	210
11 choose 4	330
12 choose 4	495
13 choose 4	715
14 choose 4	1,001
15 choose 4	1,365

Recalculate with different values ↑

FAQ

What is 8 choose 4?

8 choose 4 is 70

Why is 8 choose 4 the largest number in row 8?

In row 8 of Pascal's triangle the numbers grow towards the middle and shrink after it, because n choose k = n choose (n − k). With an even n the middle is k = 4, so 8 choose 4 = 70 is the largest: 8 choose 3 is only 56.

How many ways are there if order matters?

P(8, 4) = 1,680. Each of the 70 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.