18 Choose 4

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

What is 18 choose 4?

Answer

18 choose 4 is
3,060

Order doesn't matter, no repeats: 3,060 ways to choose 4 of 18 items.

C(18, 4) = 18! / (4! · 14!)

= (18 × 17 × 16 × 15) / (4 × 3 × 2 × 1)
= 73,440 / 24

= 3,060

If order matters (permutations): P(18, 4) = 18 × 17 × 16 × 15 = 73,440 — each combination in 4! = 24 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 4 for other n

n choose 4Answer
7 choose 435
8 choose 470
9 choose 4126
10 choose 4210
11 choose 4330
12 choose 4495
13 choose 4715
14 choose 41,001
15 choose 41,365
16 choose 41,820
17 choose 42,380
18 choose 43,060
19 choose 43,876
20 choose 44,845
24 choose 410,626

FAQ

What is 18 choose 4?

18 choose 4 is 3,060

Why is 18 choose 4 the same as 18 choose 14?

Every way to choose 4 of 18 items leaves exactly 14 behind, so choosing 4 and choosing which 14 to leave out are the same count: 18 choose 4 = 18 choose 14 = 3,060. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(18, 4) = 73,440. Each of the 3,060 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also