15 Choose 5

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

What is 15 choose 5?

Answer

15 choose 5 is
3,003

Order doesn't matter, no repeats: 3,003 ways to choose 5 of 15 items.

C(15, 5) = 15! / (5! · 10!)

= (15 × 14 × 13 × 12 × 11) / (5 × 4 × 3 × 2 × 1)
= 360,360 / 120

= 3,003

If order matters (permutations): P(15, 5) = 15 × 14 × 13 × 12 × 11 = 360,360 — each combination in 5! = 120 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 5 for other n

n choose 5Answer
6 choose 56
7 choose 521
8 choose 556
9 choose 5126
10 choose 5252
11 choose 5462
12 choose 5792
13 choose 51,287
14 choose 52,002
15 choose 53,003
16 choose 54,368
17 choose 56,188
18 choose 58,568
19 choose 511,628
20 choose 515,504

FAQ

What is 15 choose 5?

15 choose 5 is 3,003

Why is 15 choose 5 the same as 15 choose 10?

Every way to choose 5 of 15 items leaves exactly 10 behind, so choosing 5 and choosing which 10 to leave out are the same count: 15 choose 5 = 15 choose 10 = 3,003. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(15, 5) = 360,360. Each of the 3,003 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also