12 Choose 5

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

What is 12 choose 5?

Answer

12 choose 5 is
792

Order doesn't matter, no repeats: 792 ways to choose 5 of 12 items.

C(12, 5) = 12! / (5! · 7!)

= (12 × 11 × 10 × 9 × 8) / (5 × 4 × 3 × 2 × 1)
= 95,040 / 120

= 792

If order matters (permutations): P(12, 5) = 12 × 11 × 10 × 9 × 8 = 95,040 — each combination in 5! = 120 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 5 for other n

n choose 5Answer
5 choose 51
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

FAQ

What is 12 choose 5?

12 choose 5 is 792

Why is 12 choose 5 the same as 12 choose 7?

Every way to choose 5 of 12 items leaves exactly 7 behind, so choosing 5 and choosing which 7 to leave out are the same count: 12 choose 5 = 12 choose 7 = 792. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(12, 5) = 95,040. Each of the 792 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also