15 Choose 15

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

What is 15 choose 15?

Answer

15 choose 15 is
1

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

There is exactly one way: take all.

C(15, 15) = 15! / (15! · 0!)

= 1

0! = 1 (an empty product), so 15! cancels out completely.

If order matters (permutations): P(15, 15) = 15 × 14 × 13 × … × 1 = 1,307,674,368,000 — each combination in 15! = 1,307,674,368,000 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 15 for other n

n choose 15Answer
15 choose 151
16 choose 1516
17 choose 15136
18 choose 15816
19 choose 153,876
20 choose 1515,504

FAQ

What is 15 choose 15?

15 choose 15 is 1

Why is 15 choose 15 the same as 15 choose 0?

Every way to choose 15 of 15 items leaves exactly 0 behind, so choosing 15 and choosing which 0 to leave out are the same count: 15 choose 15 = 15 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(15, 15) = 1,307,674,368,000. The only combination — all 15 items — can be put in order in 15! = 1,307,674,368,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also