16 Choose 12

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

What is 16 choose 12?

Answer

16 choose 12 is
1,820

Order doesn't matter, no repeats: 1,820 ways to choose 12 of 16 items.

Choosing 12 of 16 is the same as leaving 4 out: C(16, 12) = C(16, 4).

C(16, 12) = 16! / (12! · 4!)

= C(16, 4)

= (16 × 15 × 14 × 13) / (4 × 3 × 2 × 1)
= 43,680 / 24

= 1,820

If order matters (permutations): P(16, 12) = 16 × 15 × 14 × … × 5 = 871,782,912,000 — each combination in 12! = 479,001,600 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 12 for other n

n choose 12Answer
12 choose 121
13 choose 1213
14 choose 1291
15 choose 12455
16 choose 121,820
17 choose 126,188
18 choose 1218,564
19 choose 1250,388
20 choose 12125,970

FAQ

What is 16 choose 12?

16 choose 12 is 1,820

Why is 16 choose 12 the same as 16 choose 4?

Every way to choose 12 of 16 items leaves exactly 4 behind, so choosing 12 and choosing which 4 to leave out are the same count: 16 choose 12 = 16 choose 4 = 1,820. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(16, 12) = 871,782,912,000. Each of the 1,820 combinations can be put in order in 12! = 479,001,600 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also