13 Choose 6

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

What is 13 choose 6?

Answer

13 choose 6 is
1,716

Order doesn't matter, no repeats: 1,716 ways to choose 6 of 13 items.

C(13, 6) = 13! / (6! · 7!)

= (13 × 12 × 11 × 10 × 9 × 8) / (6 × 5 × 4 × 3 × 2 × 1)
= 1,235,520 / 720

= 1,716

If order matters (permutations): P(13, 6) = 13 × 12 × 11 × 10 × 9 × 8 = 1,235,520 — each combination in 6! = 720 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 6 for other n

n choose 6Answer
6 choose 61
7 choose 67
8 choose 628
9 choose 684
10 choose 6210
11 choose 6462
12 choose 6924
13 choose 61,716
14 choose 63,003
15 choose 65,005
16 choose 68,008
17 choose 612,376
18 choose 618,564
19 choose 627,132
20 choose 638,760

FAQ

What is 13 choose 6?

13 choose 6 is 1,716

Why is 13 choose 6 the same as 13 choose 7?

Every way to choose 6 of 13 items leaves exactly 7 behind, so choosing 6 and choosing which 7 to leave out are the same count: 13 choose 6 = 13 choose 7 = 1,716. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(13, 6) = 1,235,520. Each of the 1,716 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also