19 Choose 17

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

What is 19 choose 17?

Answer

19 choose 17 is
171

Order doesn't matter, no repeats: 171 ways to choose 17 of 19 items.

Choosing 17 of 19 is the same as leaving 2 out: C(19, 17) = C(19, 2).

C(19, 17) = 19! / (17! · 2!)

= C(19, 2)

= (19 × 18) / (2 × 1)
= 342 / 2

= 171

If order matters (permutations): P(19, 17) = 19 × 18 × 17 × … × 3 = 60,822,550,204,416,000 — each combination in 17! = 355,687,428,096,000 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 17 for other n

n choose 17Answer
17 choose 171
18 choose 1718
19 choose 17171
20 choose 171,140

FAQ

What is 19 choose 17?

19 choose 17 is 171

Why is 19 choose 17 the same as 19 choose 2?

Every way to choose 17 of 19 items leaves exactly 2 behind, so choosing 17 and choosing which 2 to leave out are the same count: 19 choose 17 = 19 choose 2 = 171. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(19, 17) = 60,822,550,204,416,000. Each of the 171 combinations can be put in order in 17! = 355,687,428,096,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also