13 Choose 1

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

What is 13 choose 1?

Answer

13 choose 1 is
13

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

C(13, 1) = 13! / (1! · 12!)

= 13 / 1

= 13

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 1 for other n

n choose 1Answer
6 choose 16
7 choose 17
8 choose 18
9 choose 19
10 choose 110
11 choose 111
12 choose 112
13 choose 113
14 choose 114
15 choose 115
16 choose 116
17 choose 117
18 choose 118
19 choose 119
20 choose 120

FAQ

What is 13 choose 1?

13 choose 1 is 13

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

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

How many ways are there if order matters?

The same 13: with 1 chosen item there is only one order, so P(13, 1) = 13 choose 1 = 13. Order starts to matter from 2 items on: n × (n − 1) arrangements.

See Also