18 Choose 18

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

What is 18 choose 18?

Answer

18 choose 18 is
1

Order doesn't matter, no repeats: 1 way to choose 18 of 18 items.

There is exactly one way: take all.

C(18, 18) = 18! / (18! · 0!)

= 1

0! = 1 (an empty product), so 18! cancels out completely.

If order matters (permutations): P(18, 18) = 18 × 17 × 16 × … × 1 = 6,402,373,705,728,000 — each combination in 18! = 6,402,373,705,728,000 orders.

Row 18 of Pascal's triangle
k18 choose k
01
118
2153
3816
43,060
58,568
618,564
731,824
843,758
948,620
1043,758
1131,824
1218,564
138,568
143,060
15816
16153
1718
181

Row sum: 218 = 262,144 — all subsets of 18 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 18 choose 18?

18 choose 18 is 1

Why is 18 choose 18 the same as 18 choose 0?

Every way to choose 18 of 18 items leaves exactly 0 behind, so choosing 18 and choosing which 0 to leave out are the same count: 18 choose 18 = 18 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(18, 18) = 6,402,373,705,728,000. The only combination — all 18 items — 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