15 Choose 14

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

What is 15 choose 14?

Answer

15 choose 14 is
15

Order doesn't matter, no repeats: 15 ways to choose 14 of 15 items.

Choosing 14 of 15 is the same as leaving 1 out: C(15, 14) = C(15, 1).

C(15, 14) = 15! / (14! · 1!)

= C(15, 1)

= 15 / 1

= 15

If order matters (permutations): P(15, 14) = 15 × 14 × 13 × … × 2 = 1,307,674,368,000 — each combination in 14! = 87,178,291,200 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 14 for other n

n choose 14Answer
14 choose 141
15 choose 1415
16 choose 14120
17 choose 14680
18 choose 143,060
19 choose 1411,628
20 choose 1438,760

FAQ

What is 15 choose 14?

15 choose 14 is 15

Why is 15 choose 14 the same as 15 choose 1?

Every way to choose 14 of 15 items leaves exactly 1 behind, so choosing 14 and choosing which one to leave out are the same count: 15 choose 14 = 15 choose 1 = 15. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(15, 14) = 1,307,674,368,000. Each of the 15 combinations can be put in order in 14! = 87,178,291,200 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also