13 Choose 8

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

What is 13 choose 8?

Answer

13 choose 8 is
1,287

Order doesn't matter, no repeats: 1,287 ways to choose 8 of 13 items.

Choosing 8 of 13 is the same as leaving 5 out: C(13, 8) = C(13, 5).

C(13, 8) = 13! / (8! · 5!)

= C(13, 5)

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

= 1,287

If order matters (permutations): P(13, 8) = 13 × 12 × 11 × … × 6 = 51,891,840 — each combination in 8! = 40,320 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 8 for other n

n choose 8Answer
8 choose 81
9 choose 89
10 choose 845
11 choose 8165
12 choose 8495
13 choose 81,287
14 choose 83,003
15 choose 86,435
16 choose 812,870
17 choose 824,310
18 choose 843,758
19 choose 875,582
20 choose 8125,970

FAQ

What is 13 choose 8?

13 choose 8 is 1,287

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

Every way to choose 8 of 13 items leaves exactly 5 behind, so choosing 8 and choosing which 5 to leave out are the same count: 13 choose 8 = 13 choose 5 = 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, 8) = 51,891,840. Each of the 1,287 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also