19 Choose 7

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

What is 19 choose 7?

Answer

19 choose 7 is
50,388

Order doesn't matter, no repeats: 50,388 ways to choose 7 of 19 items.

C(19, 7) = 19! / (7! · 12!)

= (19 × 18 × 17 × … × 13) / (7 × 6 × 5 × … × 1)

7 factors on top and bottom

= 253,955,520 / 5,040

= 50,388

If order matters (permutations): P(19, 7) = 19 × 18 × 17 × … × 13 = 253,955,520 — each combination in 7! = 5,040 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 7 for other n

n choose 7Answer
7 choose 71
8 choose 78
9 choose 736
10 choose 7120
11 choose 7330
12 choose 7792
13 choose 71,716
14 choose 73,432
15 choose 76,435
16 choose 711,440
17 choose 719,448
18 choose 731,824
19 choose 750,388
20 choose 777,520

FAQ

What is 19 choose 7?

19 choose 7 is 50,388

Why is 19 choose 7 the same as 19 choose 12?

Every way to choose 7 of 19 items leaves exactly 12 behind, so choosing 7 and choosing which 12 to leave out are the same count: 19 choose 7 = 19 choose 12 = 50,388. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 7) = 253,955,520. Each of the 50,388 combinations can be put in order in 7! = 5,040 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also