13 Choose 9

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Total items (n)
Items chosen (k)

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)

= (13 × 12 × 11 × 10) / (4 × 3 × 2 × 1)
= 17,160 / 24

= 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
k13 choose k
01
113
278
3286
4715
51,287
61,716
71,716
81,287
9715
10286
1178
1213
131

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

See Also