13 Choose 5

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

What is 13 choose 5?

Answer

13 choose 5 is
1,287

Order doesn't matter, no repeats: 1,287 ways to choose 5 of 13 items.

C(13, 5) = 13! / (5! · 8!)

= (13 × 12 × 11 × 10 × 9) / (5 × 4 × 3 × 2 × 1)
= 154,440 / 120

= 1,287

If order matters (permutations): P(13, 5) = 13 × 12 × 11 × 10 × 9 = 154,440 — each combination in 5! = 120 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 5 for other n

n choose 5Answer
6 choose 56
7 choose 521
8 choose 556
9 choose 5126
10 choose 5252
11 choose 5462
12 choose 5792
13 choose 51,287
14 choose 52,002
15 choose 53,003
16 choose 54,368
17 choose 56,188
18 choose 58,568
19 choose 511,628
20 choose 515,504

FAQ

What is 13 choose 5?

13 choose 5 is 1,287

Why is 13 choose 5 the same as 13 choose 8?

Every way to choose 5 of 13 items leaves exactly 8 behind, so choosing 5 and choosing which 8 to leave out are the same count: 13 choose 5 = 13 choose 8 = 1,287. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(13, 5) = 154,440. Each of the 1,287 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also