13 Choose 13

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

What is 13 choose 13?

Answer

13 choose 13 is
1

Order doesn't matter, no repeats: 1 way to choose 13 of 13 items.

There is exactly one way: take all.

C(13, 13) = 13! / (13! · 0!)

= 1

0! = 1 (an empty product), so 13! cancels out completely.

If order matters (permutations): P(13, 13) = 13 × 12 × 11 × … × 1 = 6,227,020,800 — each combination in 13! = 6,227,020,800 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 13 for other n

n choose 13Answer
13 choose 131
14 choose 1314
15 choose 13105
16 choose 13560
17 choose 132,380
18 choose 138,568
19 choose 1327,132
20 choose 1377,520

FAQ

What is 13 choose 13?

13 choose 13 is 1

Why is 13 choose 13 the same as 13 choose 0?

Every way to choose 13 of 13 items leaves exactly 0 behind, so choosing 13 and choosing which 0 to leave out are the same count: 13 choose 13 = 13 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(13, 13) = 6,227,020,800. The only combination — all 13 items — can be put in order in 13! = 6,227,020,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also