15 Choose 3

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

What is 15 choose 3?

Answer

15 choose 3 is
455

Order doesn't matter, no repeats: 455 ways to choose 3 of 15 items.

C(15, 3) = 15! / (3! · 12!)

= (15 × 14 × 13) / (3 × 2 × 1)
= 2,730 / 6

= 455

If order matters (permutations): P(15, 3) = 15 × 14 × 13 = 2,730 — each combination in 3! = 6 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 3 for other n

n choose 3Answer
8 choose 356
9 choose 384
10 choose 3120
11 choose 3165
12 choose 3220
13 choose 3286
14 choose 3364
15 choose 3455
16 choose 3560
17 choose 3680
18 choose 3816
19 choose 3969
20 choose 31,140
25 choose 32,300
40 choose 39,880

FAQ

What is 15 choose 3?

15 choose 3 is 455

Why is 15 choose 3 the same as 15 choose 12?

Every way to choose 3 of 15 items leaves exactly 12 behind, so choosing 3 and choosing which 12 to leave out are the same count: 15 choose 3 = 15 choose 12 = 455. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(15, 3) = 2,730. Each of the 455 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also