20 Choose 12

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

What is 20 choose 12?

Answer

20 choose 12 is
125,970

Order doesn't matter, no repeats: 125,970 ways to choose 12 of 20 items.

Choosing 12 of 20 is the same as leaving 8 out: C(20, 12) = C(20, 8).

C(20, 12) = 20! / (12! · 8!)

= C(20, 8)

= (20 × 19 × 18 × … × 13) / (8 × 7 × 6 × … × 1)

8 factors on top and bottom

= 5,079,110,400 / 40,320

= 125,970

If order matters (permutations): P(20, 12) = 20 × 19 × 18 × … × 9 = 60,339,831,552,000 — each combination in 12! = 479,001,600 orders.

Row 20 of Pascal's triangle
k20 choose k
01
120
2190
31,140
44,845
515,504
638,760
777,520
8125,970
9167,960
10184,756
11167,960
12125,970
1377,520
1438,760
1515,504
164,845
171,140
18190
1920
201

Row sum: 220 = 1,048,576 — all subsets of 20 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 20 choose 12?

20 choose 12 is 125,970

Why is 20 choose 12 the same as 20 choose 8?

Every way to choose 12 of 20 items leaves exactly 8 behind, so choosing 12 and choosing which 8 to leave out are the same count: 20 choose 12 = 20 choose 8 = 125,970. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(20, 12) = 60,339,831,552,000. Each of the 125,970 combinations can be put in order in 12! = 479,001,600 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also