18 Choose 14

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

What is 18 choose 14?

Answer

18 choose 14 is
3,060

Order doesn't matter, no repeats: 3,060 ways to choose 14 of 18 items.

Choosing 14 of 18 is the same as leaving 4 out: C(18, 14) = C(18, 4).

C(18, 14) = 18! / (14! · 4!)

= C(18, 4)

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

= 3,060

If order matters (permutations): P(18, 14) = 18 × 17 × 16 × … × 5 = 266,765,571,072,000 — each combination in 14! = 87,178,291,200 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 14 for other n

n choose 14Answer
14 choose 141
15 choose 1415
16 choose 14120
17 choose 14680
18 choose 143,060
19 choose 1411,628
20 choose 1438,760

FAQ

What is 18 choose 14?

18 choose 14 is 3,060

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

Every way to choose 14 of 18 items leaves exactly 4 behind, so choosing 14 and choosing which 4 to leave out are the same count: 18 choose 14 = 18 choose 4 = 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, 14) = 266,765,571,072,000. Each of the 3,060 combinations can be put in order in 14! = 87,178,291,200 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also