19 Choose 10

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

What is 19 choose 10?

Answer

19 choose 10 is
92,378

Order doesn't matter, no repeats: 92,378 ways to choose 10 of 19 items.

Choosing 10 of 19 is the same as leaving 9 out: C(19, 10) = C(19, 9).

C(19, 10) = 19! / (10! · 9!)

= C(19, 9)

= (19 × 18 × 17 × … × 11) / (9 × 8 × 7 × … × 1)

9 factors on top and bottom

= 33,522,128,640 / 362,880

= 92,378

If order matters (permutations): P(19, 10) = 19 × 18 × 17 × … × 10 = 335,221,286,400 — each combination in 10! = 3,628,800 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 10 for other n

n choose 10Answer
2 choose 100
10 choose 101
11 choose 1011
12 choose 1066
13 choose 10286
14 choose 101,001
15 choose 103,003
16 choose 108,008
17 choose 1019,448
18 choose 1043,758
19 choose 1092,378
20 choose 10184,756
100 choose 1017,310,309,456,440

FAQ

What is 19 choose 10?

19 choose 10 is 92,378

Why is 19 choose 10 the same as 19 choose 9?

Every way to choose 10 of 19 items leaves exactly 9 behind, so choosing 10 and choosing which 9 to leave out are the same count: 19 choose 10 = 19 choose 9 = 92,378. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 10) = 335,221,286,400. Each of the 92,378 combinations can be put in order in 10! = 3,628,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also