9 Choose 8

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

What is 9 choose 8?

Answer

9 choose 8 is
9

Order doesn't matter, no repeats: 9 ways to choose 8 of 9 items.

Choosing 8 of 9 is the same as leaving 1 out: C(9, 8) = C(9, 1).

C(9, 8) = 9! / (8! · 1!)

= C(9, 1)

= 9 / 1

= 9

If order matters (permutations): P(9, 8) = 9 × 8 × 7 × … × 2 = 362,880 — each combination in 8! = 40,320 orders.

Row 9 of Pascal's triangle
k9 choose k
01
19
236
384
4126
5126
684
736
89
91

Row sum: 29 = 512 — all subsets of 9 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 9 choose 8?

9 choose 8 is 9

Why is 9 choose 8 the same as 9 choose 1?

Every way to choose 8 of 9 items leaves exactly 1 behind, so choosing 8 and choosing which one to leave out are the same count: 9 choose 8 = 9 choose 1 = 9. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(9, 8) = 362,880. Each of the 9 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also