8 Choose 4

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

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!)

= (8 × 7 × 6 × 5) / (4 × 3 × 2 × 1)
= 1,680 / 24

= 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
k8 choose k
01
18
228
356
470
556
628
78
81

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

See Also

Recalculate with different values ↑

n choose 4 for other n

n choose 4Answer
1 choose 40
2 choose 40
3 choose 40
4 choose 41
5 choose 45
6 choose 415
7 choose 435
8 choose 470
9 choose 4126
10 choose 4210
11 choose 4330
12 choose 4495
13 choose 4715
14 choose 41,001
15 choose 41,365

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)!.

See Also