10 Choose 8

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

What is 10 choose 8?

Answer

10 choose 8 is
45

Order doesn't matter, no repeats: 45 ways to choose 8 of 10 items.

Choosing 8 of 10 is the same as leaving 2 out: C(10, 8) = C(10, 2).

C(10, 8) = 10! / (8! · 2!)

= C(10, 2)

= (10 × 9) / (2 × 1)
= 90 / 2

= 45

If order matters (permutations): P(10, 8) = 10 × 9 × 8 × … × 3 = 1,814,400 — each combination in 8! = 40,320 orders.

Row 10 of Pascal's triangle
k10 choose k
01
110
245
3120
4210
5252
6210
7120
845
910
101

Row sum: 210 = 1,024 — all subsets of 10 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 10 choose 8?

10 choose 8 is 45

Why is 10 choose 8 the same as 10 choose 2?

Every way to choose 8 of 10 items leaves exactly 2 behind, so choosing 8 and choosing which 2 to leave out are the same count: 10 choose 8 = 10 choose 2 = 45. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(10, 8) = 1,814,400. Each of the 45 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also