19 Choose 12

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

What is 19 choose 12?

Answer

19 choose 12 is
50,388

Order doesn't matter, no repeats: 50,388 ways to choose 12 of 19 items.

Choosing 12 of 19 is the same as leaving 7 out: C(19, 12) = C(19, 7).

C(19, 12) = 19! / (12! · 7!)

= C(19, 7)

= (19 × 18 × 17 × … × 13) / (7 × 6 × 5 × … × 1)

7 factors on top and bottom

= 253,955,520 / 5,040

= 50,388

If order matters (permutations): P(19, 12) = 19 × 18 × 17 × … × 8 = 24,135,932,620,800 — each combination in 12! = 479,001,600 orders.

Row 19 of Pascal's triangle
k19 choose k
01
119
2171
3969
43,876
511,628
627,132
750,388
875,582
992,378
1092,378
1175,582
1250,388
1327,132
1411,628
153,876
16969
17171
1819
191

Row sum: 219 = 524,288 — all subsets of 19 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 19 choose 12?

19 choose 12 is 50,388

Why is 19 choose 12 the same as 19 choose 7?

Every way to choose 12 of 19 items leaves exactly 7 behind, so choosing 12 and choosing which 7 to leave out are the same count: 19 choose 12 = 19 choose 7 = 50,388. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 12) = 24,135,932,620,800. Each of the 50,388 combinations can be put in order in 12! = 479,001,600 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also