20 Choose 8

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

What is 20 choose 8?

Answer

20 choose 8 is
125,970

Order doesn't matter, no repeats: 125,970 ways to choose 8 of 20 items.

C(20, 8) = 20! / (8! · 12!)

= (20 × 19 × 18 × … × 13) / (8 × 7 × 6 × … × 1)

8 factors on top and bottom

= 5,079,110,400 / 40,320

= 125,970

If order matters (permutations): P(20, 8) = 20 × 19 × 18 × … × 13 = 5,079,110,400 — each combination in 8! = 40,320 orders.

Row 20 of Pascal's triangle
k20 choose k
01
120
2190
31,140
44,845
515,504
638,760
777,520
8125,970
9167,960
10184,756
11167,960
12125,970
1377,520
1438,760
1515,504
164,845
171,140
18190
1920
201

Row sum: 220 = 1,048,576 — all subsets of 20 items.

See Also

Recalculate with different values ↑

n choose 8 for other n

n choose 8Answer
8 choose 81
9 choose 89
10 choose 845
11 choose 8165
12 choose 8495
13 choose 81,287
14 choose 83,003
15 choose 86,435
16 choose 812,870
17 choose 824,310
18 choose 843,758
19 choose 875,582
20 choose 8125,970

FAQ

What is 20 choose 8?

20 choose 8 is 125,970

Why is 20 choose 8 the same as 20 choose 12?

Every way to choose 8 of 20 items leaves exactly 12 behind, so choosing 8 and choosing which 12 to leave out are the same count: 20 choose 8 = 20 choose 12 = 125,970. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(20, 8) = 5,079,110,400. Each of the 125,970 combinations can be put in order in 8! = 40,320 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also