19 Choose 9

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

What is 19 choose 9?

Answer

19 choose 9 is
92,378

Order doesn't matter, no repeats: 92,378 ways to choose 9 of 19 items.

C(19, 9) = 19! / (9! · 10!)

= (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, 9) = 19 × 18 × 17 × … × 11 = 33,522,128,640 — each combination in 9! = 362,880 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 9 for other n

n choose 9Answer
9 choose 91
10 choose 910
11 choose 955
12 choose 9220
13 choose 9715
14 choose 92,002
15 choose 95,005
16 choose 911,440
17 choose 924,310
18 choose 948,620
19 choose 992,378
20 choose 9167,960

FAQ

What is 19 choose 9?

19 choose 9 is 92,378

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

Every way to choose 9 of 19 items leaves exactly 10 behind, so choosing 9 and choosing which 10 to leave out are the same count: 19 choose 9 = 19 choose 10 = 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, 9) = 33,522,128,640. Each of the 92,378 combinations can be put in order in 9! = 362,880 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also