19 Choose 16

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

What is 19 choose 16?

Answer

19 choose 16 is
969

Order doesn't matter, no repeats: 969 ways to choose 16 of 19 items.

Choosing 16 of 19 is the same as leaving 3 out: C(19, 16) = C(19, 3).

C(19, 16) = 19! / (16! · 3!)

= C(19, 3)

= (19 × 18 × 17) / (3 × 2 × 1)
= 5,814 / 6

= 969

If order matters (permutations): P(19, 16) = 19 × 18 × 17 × … × 4 = 20,274,183,401,472,000 — each combination in 16! = 20,922,789,888,000 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 16 for other n

n choose 16Answer
16 choose 161
17 choose 1617
18 choose 16153
19 choose 16969
20 choose 164,845

FAQ

What is 19 choose 16?

19 choose 16 is 969

Why is 19 choose 16 the same as 19 choose 3?

Every way to choose 16 of 19 items leaves exactly 3 behind, so choosing 16 and choosing which 3 to leave out are the same count: 19 choose 16 = 19 choose 3 = 969. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 16) = 20,274,183,401,472,000. Each of the 969 combinations can be put in order in 16! = 20,922,789,888,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also