15 Choose 8

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

What is 15 choose 8?

Answer

15 choose 8 is
6,435

Order doesn't matter, no repeats: 6,435 ways to choose 8 of 15 items.

Choosing 8 of 15 is the same as leaving 7 out: C(15, 8) = C(15, 7).

C(15, 8) = 15! / (8! · 7!)

= C(15, 7)

= (15 × 14 × 13 × … × 9) / (7 × 6 × 5 × … × 1)

7 factors on top and bottom

= 32,432,400 / 5,040

= 6,435

If order matters (permutations): P(15, 8) = 15 × 14 × 13 × … × 8 = 259,459,200 — each combination in 8! = 40,320 orders.

Row 15 of Pascal's triangle
k15 choose k
01
115
2105
3455
41,365
53,003
65,005
76,435
86,435
95,005
103,003
111,365
12455
13105
1415
151

Row sum: 215 = 32,768 — all subsets of 15 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 15 choose 8?

15 choose 8 is 6,435

Why is 15 choose 8 the same as 15 choose 7?

Every way to choose 8 of 15 items leaves exactly 7 behind, so choosing 8 and choosing which 7 to leave out are the same count: 15 choose 8 = 15 choose 7 = 6,435. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(15, 8) = 259,459,200. Each of the 6,435 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also