9 Choose 9

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

What is 9 choose 9?

Answer

9 choose 9 is
1

Order doesn't matter, no repeats: 1 way to choose 9 of 9 items.

There is exactly one way: take all.

C(9, 9) = 9! / (9! · 0!)

= 1

0! = 1 (an empty product), so 9! cancels out completely.

If order matters (permutations): P(9, 9) = 9 × 8 × 7 × … × 1 = 362,880 — each combination in 9! = 362,880 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 9 for other n

n choose 9Answer
9 choose 91
10 choose 910
11 choose 955
12 choose 9220
13 choose 9715
14 choose 92,002
15 choose 95,005
16 choose 911,440
17 choose 924,310
18 choose 948,620
19 choose 992,378
20 choose 9167,960

FAQ

What is 9 choose 9?

9 choose 9 is 1

Why is 9 choose 9 the same as 9 choose 0?

Every way to choose 9 of 9 items leaves exactly 0 behind, so choosing 9 and choosing which 0 to leave out are the same count: 9 choose 9 = 9 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(9, 9) = 362,880. The only combination — all 9 items — can be put in order in 9! = 362,880 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also