20 Choose 14

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

What is 20 choose 14?

Answer

20 choose 14 is
38,760

Order doesn't matter, no repeats: 38,760 ways to choose 14 of 20 items.

Choosing 14 of 20 is the same as leaving 6 out: C(20, 14) = C(20, 6).

C(20, 14) = 20! / (14! · 6!)

= C(20, 6)

= (20 × 19 × 18 × 17 × 16 × 15) / (6 × 5 × 4 × 3 × 2 × 1)
= 27,907,200 / 720

= 38,760

If order matters (permutations): P(20, 14) = 20 × 19 × 18 × … × 7 = 3,379,030,566,912,000 — each combination in 14! = 87,178,291,200 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 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 20 choose 14?

20 choose 14 is 38,760

Why is 20 choose 14 the same as 20 choose 6?

Every way to choose 14 of 20 items leaves exactly 6 behind, so choosing 14 and choosing which 6 to leave out are the same count: 20 choose 14 = 20 choose 6 = 38,760. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(20, 14) = 3,379,030,566,912,000. Each of the 38,760 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