20 Choose 18

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

What is 20 choose 18?

Answer

20 choose 18 is
190

Order doesn't matter, no repeats: 190 ways to choose 18 of 20 items.

Choosing 18 of 20 is the same as leaving 2 out: C(20, 18) = C(20, 2).

C(20, 18) = 20! / (18! · 2!)

= C(20, 2)

= (20 × 19) / (2 × 1)
= 380 / 2

= 190

If order matters (permutations): P(20, 18) = 20 × 19 × 18 × … × 3 = 1,216,451,004,088,320,000 — each combination in 18! = 6,402,373,705,728,000 orders.

Row 20 of Pascal's triangle
k20 choose k
01
120
2190
31,140
44,845
515,504
638,760
777,520
8125,970
9167,960
10184,756
11167,960
12125,970
1377,520
1438,760
1515,504
164,845
171,140
18190
1920
201

Row sum: 220 = 1,048,576 — all subsets of 20 items.

See Also

Recalculate with different values ↑

n choose 18 for other n

n choose 18Answer
18 choose 181
19 choose 1819
20 choose 18190

FAQ

What is 20 choose 18?

20 choose 18 is 190

Why is 20 choose 18 the same as 20 choose 2?

Every way to choose 18 of 20 items leaves exactly 2 behind, so choosing 18 and choosing which 2 to leave out are the same count: 20 choose 18 = 20 choose 2 = 190. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(20, 18) = 1,216,451,004,088,320,000. Each of the 190 combinations can be put in order in 18! = 6,402,373,705,728,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also