13 Choose 2

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

What is 13 choose 2?

Answer

13 choose 2 is
78

Order doesn't matter, no repeats: 78 ways to choose 2 of 13 items.

C(13, 2) = 13! / (2! · 11!)

= (13 × 12) / (2 × 1)
= 156 / 2

= 78

If order matters (permutations): P(13, 2) = 13 × 12 = 156 — each combination in 2! = 2 orders.

Row 13 of Pascal's triangle
k13 choose k
01
113
278
3286
4715
51,287
61,716
71,716
81,287
9715
10286
1178
1213
131

Row sum: 213 = 8,192 — all subsets of 13 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 13 choose 2?

13 choose 2 is 78

Why is 13 choose 2 the same as 13 choose 11?

Every way to choose 2 of 13 items leaves exactly 11 behind, so choosing 2 and choosing which 11 to leave out are the same count: 13 choose 2 = 13 choose 11 = 78. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(13, 2) = 156. Each of the 78 combinations can be put in order in 2! = 2 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also