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13 Choose 9

Combination Calculator

What is 13 choose 9?

Answer

13 choose 9 is

715

Order doesn't matter, no repeats: 715 ways to choose 9 of 13 items.

Choosing 9 of 13 is the same as leaving 4 out: C(13, 9) = C(13, 4).

C(13, 9) = 13! / (9! · 4!)

= C(13, 4)

= 715

If order matters (permutations): P(13, 9) = 13 × 12 × 11 × … × 5 = 259,459,200 — each combination in 9! = 362,880 orders.

Row 13 of Pascal's triangle
k	13 choose k
0	1
1	13
2	78
3	286
4	715
5	1,287
6	1,716
7	1,716
8	1,287
9	715
10	286
11	78
12	13
13	1

Row sum: 2¹³ = 8,192 — all subsets of 13 items.

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https://calculat.io/en/number/combinations/13--9

<a href="https://calculat.io/en/number/combinations/13--9">13 Choose 9: Combinations C(13, 9) - Calculatio</a>

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13 Choose 9: Combinations C(13, 9). 13 choose 9 = 715: the number of ways to choose 9 of 13 items when order doesn't matter and nothing repeats. C(13, 9) = (13 × 12 × 11 × 10) / (4 × 3 × 2 × 1).

https://calculat.io/en/number/combinations/13--9/generated.jpg

n choose 9 for other n

n choose 9	Answer
9 choose 9	1
10 choose 9	10
11 choose 9	55
12 choose 9	220
13 choose 9	715
14 choose 9	2,002
15 choose 9	5,005
16 choose 9	11,440
17 choose 9	24,310
18 choose 9	48,620
19 choose 9	92,378
20 choose 9	167,960

Recalculate with different values ↑

FAQ

What is 13 choose 9?

13 choose 9 is 715

Why is 13 choose 9 the same as 13 choose 4?

Every way to choose 9 of 13 items leaves exactly 4 behind, so choosing 9 and choosing which 4 to leave out are the same count: 13 choose 9 = 13 choose 4 = 715. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(13, 9) = 259,459,200. Each of the 715 combinations can be put in order in 9! = 362,880 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.