24 Choose 4

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

What is 24 choose 4?

Answer

24 choose 4 is
10,626

Order doesn't matter, no repeats: 10,626 ways to choose 4 of 24 items.

C(24, 4) = 24! / (4! · 20!)

= (24 × 23 × 22 × 21) / (4 × 3 × 2 × 1)
= 255,024 / 24

= 10,626

If order matters (permutations): P(24, 4) = 24 × 23 × 22 × 21 = 255,024 — each combination in 4! = 24 orders.

Row 24 of Pascal's triangle
k24 choose k
01
124
2276
32,024
410,626
542,504
6134,596
7346,104
……
241

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 24 choose 4?

24 choose 4 is 10,626

Why is 24 choose 4 the same as 24 choose 20?

Every way to choose 4 of 24 items leaves exactly 20 behind, so choosing 4 and choosing which 20 to leave out are the same count: 24 choose 4 = 24 choose 20 = 10,626. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(24, 4) = 255,024. Each of the 10,626 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also