13 Choose 7

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

What is 13 choose 7?

Answer

13 choose 7 is
1,716

Order doesn't matter, no repeats: 1,716 ways to choose 7 of 13 items.

Choosing 7 of 13 is the same as leaving 6 out: C(13, 7) = C(13, 6).

C(13, 7) = 13! / (7! · 6!)

= C(13, 6)

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

= 1,716

If order matters (permutations): P(13, 7) = 13 × 12 × 11 × … × 7 = 8,648,640 — each combination in 7! = 5,040 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 7 for other n

n choose 7Answer
7 choose 71
8 choose 78
9 choose 736
10 choose 7120
11 choose 7330
12 choose 7792
13 choose 71,716
14 choose 73,432
15 choose 76,435
16 choose 711,440
17 choose 719,448
18 choose 731,824
19 choose 750,388
20 choose 777,520

FAQ

What is 13 choose 7?

13 choose 7 is 1,716

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

Every way to choose 7 of 13 items leaves exactly 6 behind, so choosing 7 and choosing which 6 to leave out are the same count: 13 choose 7 = 13 choose 6 = 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, 7) = 8,648,640. Each of the 1,716 combinations can be put in order in 7! = 5,040 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also