16 Choose 15

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

What is 16 choose 15?

Answer

16 choose 15 is
16

Order doesn't matter, no repeats: 16 ways to choose 15 of 16 items.

Choosing 15 of 16 is the same as leaving 1 out: C(16, 15) = C(16, 1).

C(16, 15) = 16! / (15! · 1!)

= C(16, 1)

= 16 / 1

= 16

If order matters (permutations): P(16, 15) = 16 × 15 × 14 × … × 2 = 20,922,789,888,000 — each combination in 15! = 1,307,674,368,000 orders.

Row 16 of Pascal's triangle
k16 choose k
01
116
2120
3560
41,820
54,368
68,008
711,440
812,870
911,440
108,008
114,368
121,820
13560
14120
1516
161

Row sum: 216 = 65,536 — all subsets of 16 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 16 choose 15?

16 choose 15 is 16

Why is 16 choose 15 the same as 16 choose 1?

Every way to choose 15 of 16 items leaves exactly 1 behind, so choosing 15 and choosing which one to leave out are the same count: 16 choose 15 = 16 choose 1 = 16. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(16, 15) = 20,922,789,888,000. Each of the 16 combinations 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