19 Choose 3

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

What is 19 choose 3?

Answer

19 choose 3 is
969

Order doesn't matter, no repeats: 969 ways to choose 3 of 19 items.

C(19, 3) = 19! / (3! · 16!)

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

= 969

If order matters (permutations): P(19, 3) = 19 × 18 × 17 = 5,814 — each combination in 3! = 6 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 3 for other n

n choose 3Answer
9 choose 384
10 choose 3120
11 choose 3165
12 choose 3220
13 choose 3286
14 choose 3364
15 choose 3455
16 choose 3560
17 choose 3680
18 choose 3816
19 choose 3969
20 choose 31,140
25 choose 32,300
40 choose 39,880
100 choose 3161,700

FAQ

What is 19 choose 3?

19 choose 3 is 969

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

Every way to choose 3 of 19 items leaves exactly 16 behind, so choosing 3 and choosing which 16 to leave out are the same count: 19 choose 3 = 19 choose 16 = 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, 3) = 5,814. Each of the 969 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also