18 Choose 7

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

What is 18 choose 7?

Answer

18 choose 7 is
31,824

Order doesn't matter, no repeats: 31,824 ways to choose 7 of 18 items.

C(18, 7) = 18! / (7! · 11!)

= (18 × 17 × 16 × … × 12) / (7 × 6 × 5 × … × 1)

7 factors on top and bottom

= 160,392,960 / 5,040

= 31,824

If order matters (permutations): P(18, 7) = 18 × 17 × 16 × … × 12 = 160,392,960 — each combination in 7! = 5,040 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 7 for other n

n choose 7Answer
7 choose 71
8 choose 78
9 choose 736
10 choose 7120
11 choose 7330
12 choose 7792
13 choose 71,716
14 choose 73,432
15 choose 76,435
16 choose 711,440
17 choose 719,448
18 choose 731,824
19 choose 750,388
20 choose 777,520

FAQ

What is 18 choose 7?

18 choose 7 is 31,824

Why is 18 choose 7 the same as 18 choose 11?

Every way to choose 7 of 18 items leaves exactly 11 behind, so choosing 7 and choosing which 11 to leave out are the same count: 18 choose 7 = 18 choose 11 = 31,824. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(18, 7) = 160,392,960. Each of the 31,824 combinations can be put in order in 7! = 5,040 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also