15 Choose 12

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

What is 15 choose 12?

Answer

15 choose 12 is
455

Order doesn't matter, no repeats: 455 ways to choose 12 of 15 items.

Choosing 12 of 15 is the same as leaving 3 out: C(15, 12) = C(15, 3).

C(15, 12) = 15! / (12! · 3!)

= C(15, 3)

= (15 × 14 × 13) / (3 × 2 × 1)
= 2,730 / 6

= 455

If order matters (permutations): P(15, 12) = 15 × 14 × 13 × … × 4 = 217,945,728,000 — each combination in 12! = 479,001,600 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 12 for other n

n choose 12Answer
12 choose 121
13 choose 1213
14 choose 1291
15 choose 12455
16 choose 121,820
17 choose 126,188
18 choose 1218,564
19 choose 1250,388
20 choose 12125,970

FAQ

What is 15 choose 12?

15 choose 12 is 455

Why is 15 choose 12 the same as 15 choose 3?

Every way to choose 12 of 15 items leaves exactly 3 behind, so choosing 12 and choosing which 3 to leave out are the same count: 15 choose 12 = 15 choose 3 = 455. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(15, 12) = 217,945,728,000. Each of the 455 combinations can be put in order in 12! = 479,001,600 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also