19 Choose 14

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

What is 19 choose 14?

Answer

19 choose 14 is
11,628

Order doesn't matter, no repeats: 11,628 ways to choose 14 of 19 items.

Choosing 14 of 19 is the same as leaving 5 out: C(19, 14) = C(19, 5).

C(19, 14) = 19! / (14! · 5!)

= C(19, 5)

= (19 × 18 × 17 × 16 × 15) / (5 × 4 × 3 × 2 × 1)
= 1,395,360 / 120

= 11,628

If order matters (permutations): P(19, 14) = 19 × 18 × 17 × … × 6 = 1,013,709,170,073,600 — each combination in 14! = 87,178,291,200 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 14 for other n

n choose 14Answer
14 choose 141
15 choose 1415
16 choose 14120
17 choose 14680
18 choose 143,060
19 choose 1411,628
20 choose 1438,760

FAQ

What is 19 choose 14?

19 choose 14 is 11,628

Why is 19 choose 14 the same as 19 choose 5?

Every way to choose 14 of 19 items leaves exactly 5 behind, so choosing 14 and choosing which 5 to leave out are the same count: 19 choose 14 = 19 choose 5 = 11,628. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 14) = 1,013,709,170,073,600. Each of the 11,628 combinations can be put in order in 14! = 87,178,291,200 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also