18 Choose 10

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

What is 18 choose 10?

Answer

18 choose 10 is
43,758

Order doesn't matter, no repeats: 43,758 ways to choose 10 of 18 items.

Choosing 10 of 18 is the same as leaving 8 out: C(18, 10) = C(18, 8).

C(18, 10) = 18! / (10! · 8!)

= C(18, 8)

= (18 × 17 × 16 × … × 11) / (8 × 7 × 6 × … × 1)

8 factors on top and bottom

= 1,764,322,560 / 40,320

= 43,758

If order matters (permutations): P(18, 10) = 18 × 17 × 16 × … × 9 = 158,789,030,400 — each combination in 10! = 3,628,800 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 10 for other n

n choose 10Answer
2 choose 100
10 choose 101
11 choose 1011
12 choose 1066
13 choose 10286
14 choose 101,001
15 choose 103,003
16 choose 108,008
17 choose 1019,448
18 choose 1043,758
19 choose 1092,378
20 choose 10184,756
100 choose 1017,310,309,456,440

FAQ

What is 18 choose 10?

18 choose 10 is 43,758

Why is 18 choose 10 the same as 18 choose 8?

Every way to choose 10 of 18 items leaves exactly 8 behind, so choosing 10 and choosing which 8 to leave out are the same count: 18 choose 10 = 18 choose 8 = 43,758. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(18, 10) = 158,789,030,400. Each of the 43,758 combinations can be put in order in 10! = 3,628,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also