18 Choose 15

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

What is 18 choose 15?

Answer

18 choose 15 is
816

Order doesn't matter, no repeats: 816 ways to choose 15 of 18 items.

Choosing 15 of 18 is the same as leaving 3 out: C(18, 15) = C(18, 3).

C(18, 15) = 18! / (15! · 3!)

= C(18, 3)

= (18 × 17 × 16) / (3 × 2 × 1)
= 4,896 / 6

= 816

If order matters (permutations): P(18, 15) = 18 × 17 × 16 × … × 4 = 1,067,062,284,288,000 — each combination in 15! = 1,307,674,368,000 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 15 for other n

n choose 15Answer
15 choose 151
16 choose 1516
17 choose 15136
18 choose 15816
19 choose 153,876
20 choose 1515,504

FAQ

What is 18 choose 15?

18 choose 15 is 816

Why is 18 choose 15 the same as 18 choose 3?

Every way to choose 15 of 18 items leaves exactly 3 behind, so choosing 15 and choosing which 3 to leave out are the same count: 18 choose 15 = 18 choose 3 = 816. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(18, 15) = 1,067,062,284,288,000. Each of the 816 combinations can be put in order in 15! = 1,307,674,368,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also