8 Choose 3

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

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!)

= (8 × 7 × 6) / (3 × 2 × 1)
= 336 / 6

= 56

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

n choose 3Answer
1 choose 30
2 choose 30
3 choose 31
4 choose 34
5 choose 310
6 choose 320
7 choose 335
8 choose 356
9 choose 384
10 choose 3120
11 choose 3165
12 choose 3220
13 choose 3286
14 choose 3364
15 choose 3455

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)!.

See Also