10 Choose 9

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

What is 10 choose 9?

Answer

10 choose 9 is
10

Order doesn't matter, no repeats: 10 ways to choose 9 of 10 items.

Choosing 9 of 10 is the same as leaving 1 out: C(10, 9) = C(10, 1).

C(10, 9) = 10! / (9! · 1!)

= C(10, 1)

= 10 / 1

= 10

If order matters (permutations): P(10, 9) = 10 × 9 × 8 × … × 2 = 3,628,800 — each combination in 9! = 362,880 orders.

Row 10 of Pascal's triangle
k10 choose k
01
110
245
3120
4210
5252
6210
7120
845
910
101

Row sum: 210 = 1,024 — all subsets of 10 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 10 choose 9?

10 choose 9 is 10

Why is 10 choose 9 the same as 10 choose 1?

Every way to choose 9 of 10 items leaves exactly 1 behind, so choosing 9 and choosing which one to leave out are the same count: 10 choose 9 = 10 choose 1 = 10. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(10, 9) = 3,628,800. Each of the 10 combinations can be put in order in 9! = 362,880 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also