14 Choose 12

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

What is 14 choose 12?

Answer

14 choose 12 is
91

Order doesn't matter, no repeats: 91 ways to choose 12 of 14 items.

Choosing 12 of 14 is the same as leaving 2 out: C(14, 12) = C(14, 2).

C(14, 12) = 14! / (12! · 2!)

= C(14, 2)

= (14 × 13) / (2 × 1)
= 182 / 2

= 91

If order matters (permutations): P(14, 12) = 14 × 13 × 12 × … × 3 = 43,589,145,600 — each combination in 12! = 479,001,600 orders.

Row 14 of Pascal's triangle
k14 choose k
01
114
291
3364
41,001
52,002
63,003
73,432
83,003
92,002
101,001
11364
1291
1314
141

Row sum: 214 = 16,384 — all subsets of 14 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 14 choose 12?

14 choose 12 is 91

Why is 14 choose 12 the same as 14 choose 2?

Every way to choose 12 of 14 items leaves exactly 2 behind, so choosing 12 and choosing which 2 to leave out are the same count: 14 choose 12 = 14 choose 2 = 91. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(14, 12) = 43,589,145,600. Each of the 91 combinations can be put in order in 12! = 479,001,600 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also