13 Choose 12

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

What is 13 choose 12?

Answer

13 choose 12 is
13

Order doesn't matter, no repeats: 13 ways to choose 12 of 13 items.

Choosing 12 of 13 is the same as leaving 1 out: C(13, 12) = C(13, 1).

C(13, 12) = 13! / (12! · 1!)

= C(13, 1)

= 13 / 1

= 13

If order matters (permutations): P(13, 12) = 13 × 12 × 11 × … × 2 = 6,227,020,800 — each combination in 12! = 479,001,600 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 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 13 choose 12?

13 choose 12 is 13

Why is 13 choose 12 the same as 13 choose 1?

Every way to choose 12 of 13 items leaves exactly 1 behind, so choosing 12 and choosing which one to leave out are the same count: 13 choose 12 = 13 choose 1 = 13. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(13, 12) = 6,227,020,800. Each of the 13 combinations can be put in order in 12! = 479,001,600 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also