15 Choose 4

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

What is 15 choose 4?

Answer

15 choose 4 is
1,365

Order doesn't matter, no repeats: 1,365 ways to choose 4 of 15 items.

C(15, 4) = 15! / (4! · 11!)

= (15 × 14 × 13 × 12) / (4 × 3 × 2 × 1)
= 32,760 / 24

= 1,365

If order matters (permutations): P(15, 4) = 15 × 14 × 13 × 12 = 32,760 — each combination in 4! = 24 orders.

Row 15 of Pascal's triangle
k15 choose k
01
115
2105
3455
41,365
53,003
65,005
76,435
86,435
95,005
103,003
111,365
12455
13105
1415
151

Row sum: 215 = 32,768 — all subsets of 15 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 15 choose 4?

15 choose 4 is 1,365

Why is 15 choose 4 the same as 15 choose 11?

Every way to choose 4 of 15 items leaves exactly 11 behind, so choosing 4 and choosing which 11 to leave out are the same count: 15 choose 4 = 15 choose 11 = 1,365. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(15, 4) = 32,760. Each of the 1,365 combinations can be put in order in 4! = 24 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also