12 Choose 7

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

What is 12 choose 7?

Answer

12 choose 7 is
792

Order doesn't matter, no repeats: 792 ways to choose 7 of 12 items.

Choosing 7 of 12 is the same as leaving 5 out: C(12, 7) = C(12, 5).

C(12, 7) = 12! / (7! · 5!)

= C(12, 5)

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

= 792

If order matters (permutations): P(12, 7) = 12 × 11 × 10 × … × 6 = 3,991,680 — each combination in 7! = 5,040 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 7 for other n

n choose 7Answer
7 choose 71
8 choose 78
9 choose 736
10 choose 7120
11 choose 7330
12 choose 7792
13 choose 71,716
14 choose 73,432
15 choose 76,435
16 choose 711,440
17 choose 719,448
18 choose 731,824
19 choose 750,388
20 choose 777,520

FAQ

What is 12 choose 7?

12 choose 7 is 792

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

Every way to choose 7 of 12 items leaves exactly 5 behind, so choosing 7 and choosing which 5 to leave out are the same count: 12 choose 7 = 12 choose 5 = 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, 7) = 3,991,680. Each of the 792 combinations can be put in order in 7! = 5,040 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also