8 Choose 8

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

What is 8 choose 8?

Answer

8 choose 8 is
1

Order doesn't matter, no repeats: 1 way to choose 8 of 8 items.

There is exactly one way: take all.

C(8, 8) = 8! / (8! · 0!)

= 1

0! = 1 (an empty product), so 8! cancels out completely.

If order matters (permutations): P(8, 8) = 8 × 7 × 6 × … × 1 = 40,320 — each combination in 8! = 40,320 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 8 for other n

n choose 8Answer
8 choose 81
9 choose 89
10 choose 845
11 choose 8165
12 choose 8495
13 choose 81,287
14 choose 83,003
15 choose 86,435
16 choose 812,870
17 choose 824,310
18 choose 843,758
19 choose 875,582
20 choose 8125,970

FAQ

What is 8 choose 8?

8 choose 8 is 1

Why is 8 choose 8 the same as 8 choose 0?

Every way to choose 8 of 8 items leaves exactly 0 behind, so choosing 8 and choosing which 0 to leave out are the same count: 8 choose 8 = 8 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(8, 8) = 40,320. The only combination — all 8 items — can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also