14 Choose 2

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

What is 14 choose 2?

Answer

14 choose 2 is
91

Order doesn't matter, no repeats: 91 ways to choose 2 of 14 items.

C(14, 2) = 14! / (2! · 12!)

= (14 × 13) / (2 × 1)
= 182 / 2

= 91

If order matters (permutations): P(14, 2) = 14 × 13 = 182 — each combination in 2! = 2 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 2 for other n

n choose 2Answer
6 choose 215
7 choose 221
8 choose 228
9 choose 236
10 choose 245
11 choose 255
12 choose 266
13 choose 278
14 choose 291
15 choose 2105
16 choose 2120
17 choose 2136
18 choose 2153
19 choose 2171
20 choose 2190

FAQ

What is 14 choose 2?

14 choose 2 is 91

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

Every way to choose 2 of 14 items leaves exactly 12 behind, so choosing 2 and choosing which 12 to leave out are the same count: 14 choose 2 = 14 choose 12 = 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, 2) = 182. Each of the 91 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also