20 Choose 4

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

What is 20 choose 4?

Answer

20 choose 4 is
4,845

Order doesn't matter, no repeats: 4,845 ways to choose 4 of 20 items.

C(20, 4) = 20! / (4! · 16!)

= (20 × 19 × 18 × 17) / (4 × 3 × 2 × 1)
= 116,280 / 24

= 4,845

If order matters (permutations): P(20, 4) = 20 × 19 × 18 × 17 = 116,280 — each combination in 4! = 24 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 4 for other n

n choose 4Answer
7 choose 435
8 choose 470
9 choose 4126
10 choose 4210
11 choose 4330
12 choose 4495
13 choose 4715
14 choose 41,001
15 choose 41,365
16 choose 41,820
17 choose 42,380
18 choose 43,060
19 choose 43,876
20 choose 44,845
24 choose 410,626

FAQ

What is 20 choose 4?

20 choose 4 is 4,845

Why is 20 choose 4 the same as 20 choose 16?

Every way to choose 4 of 20 items leaves exactly 16 behind, so choosing 4 and choosing which 16 to leave out are the same count: 20 choose 4 = 20 choose 16 = 4,845. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(20, 4) = 116,280. Each of the 4,845 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also