13 Choose 4

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Total items (n)
Items chosen (k)

What is 13 choose 4?

Answer

13 choose 4 is
715

Order doesn't matter, no repeats: 715 ways to choose 4 of 13 items.

C(13, 4) = 13! / (4! · 9!)

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

= 715

If order matters (permutations): P(13, 4) = 13 × 12 × 11 × 10 = 17,160 — each combination in 4! = 24 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 4 for other n

n choose 4Answer
6 choose 415
7 choose 435
8 choose 470
9 choose 4126
10 choose 4210
11 choose 4330
12 choose 4495
13 choose 4715
14 choose 41,001
15 choose 41,365
16 choose 41,820
17 choose 42,380
18 choose 43,060
19 choose 43,876
20 choose 44,845

FAQ

What is 13 choose 4?

13 choose 4 is 715

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

Every way to choose 4 of 13 items leaves exactly 9 behind, so choosing 4 and choosing which 9 to leave out are the same count: 13 choose 4 = 13 choose 9 = 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, 4) = 17,160. Each of the 715 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also