10 Choose 4

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

What is 10 choose 4?

Answer

10 choose 4 is
210

Order doesn't matter, no repeats: 210 ways to choose 4 of 10 items.

C(10, 4) = 10! / (4! · 6!)

= (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1)
= 5,040 / 24

= 210

If order matters (permutations): P(10, 4) = 10 × 9 × 8 × 7 = 5,040 — each combination in 4! = 24 orders.

Row 10 of Pascal's triangle
k10 choose k
01
110
245
3120
4210
5252
6210
7120
845
910
101

Row sum: 210 = 1,024 — all subsets of 10 items.

See Also

Recalculate with different values ↑

n choose 4 for other n

n choose 4Answer
3 choose 40
4 choose 41
5 choose 45
6 choose 415
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

FAQ

What is 10 choose 4?

10 choose 4 is 210

Why is 10 choose 4 the same as 10 choose 6?

Every way to choose 4 of 10 items leaves exactly 6 behind, so choosing 4 and choosing which 6 to leave out are the same count: 10 choose 4 = 10 choose 6 = 210. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(10, 4) = 5,040. Each of the 210 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also