19 Choose 15

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

What is 19 choose 15?

Answer

19 choose 15 is
3,876

Order doesn't matter, no repeats: 3,876 ways to choose 15 of 19 items.

Choosing 15 of 19 is the same as leaving 4 out: C(19, 15) = C(19, 4).

C(19, 15) = 19! / (15! · 4!)

= C(19, 4)

= (19 × 18 × 17 × 16) / (4 × 3 × 2 × 1)
= 93,024 / 24

= 3,876

If order matters (permutations): P(19, 15) = 19 × 18 × 17 × … × 5 = 5,068,545,850,368,000 — each combination in 15! = 1,307,674,368,000 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 15 for other n

n choose 15Answer
15 choose 151
16 choose 1516
17 choose 15136
18 choose 15816
19 choose 153,876
20 choose 1515,504

FAQ

What is 19 choose 15?

19 choose 15 is 3,876

Why is 19 choose 15 the same as 19 choose 4?

Every way to choose 15 of 19 items leaves exactly 4 behind, so choosing 15 and choosing which 4 to leave out are the same count: 19 choose 15 = 19 choose 4 = 3,876. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 15) = 5,068,545,850,368,000. Each of the 3,876 combinations can be put in order in 15! = 1,307,674,368,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also