12 Choose 10

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

What is 12 choose 10?

Answer

12 choose 10 is
66

Order doesn't matter, no repeats: 66 ways to choose 10 of 12 items.

Choosing 10 of 12 is the same as leaving 2 out: C(12, 10) = C(12, 2).

C(12, 10) = 12! / (10! · 2!)

= C(12, 2)

= (12 × 11) / (2 × 1)
= 132 / 2

= 66

If order matters (permutations): P(12, 10) = 12 × 11 × 10 × … × 3 = 239,500,800 — each combination in 10! = 3,628,800 orders.

Row 12 of Pascal's triangle
k12 choose k
01
112
266
3220
4495
5792
6924
7792
8495
9220
1066
1112
121

Row sum: 212 = 4,096 — all subsets of 12 items.

See Also

Recalculate with different values ↑

n choose 10 for other n

n choose 10Answer
2 choose 100
10 choose 101
11 choose 1011
12 choose 1066
13 choose 10286
14 choose 101,001
15 choose 103,003
16 choose 108,008
17 choose 1019,448
18 choose 1043,758
19 choose 1092,378
20 choose 10184,756
100 choose 1017,310,309,456,440

FAQ

What is 12 choose 10?

12 choose 10 is 66

Why is 12 choose 10 the same as 12 choose 2?

Every way to choose 10 of 12 items leaves exactly 2 behind, so choosing 10 and choosing which 2 to leave out are the same count: 12 choose 10 = 12 choose 2 = 66. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(12, 10) = 239,500,800. Each of the 66 combinations can be put in order in 10! = 3,628,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also