15 Choose 7

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

What is 15 choose 7?

Answer

15 choose 7 is
6,435

Order doesn't matter, no repeats: 6,435 ways to choose 7 of 15 items.

C(15, 7) = 15! / (7! · 8!)

= (15 × 14 × 13 × … × 9) / (7 × 6 × 5 × … × 1)

7 factors on top and bottom

= 32,432,400 / 5,040

= 6,435

If order matters (permutations): P(15, 7) = 15 × 14 × 13 × … × 9 = 32,432,400 — each combination in 7! = 5,040 orders.

Row 15 of Pascal's triangle
k15 choose k
01
115
2105
3455
41,365
53,003
65,005
76,435
86,435
95,005
103,003
111,365
12455
13105
1415
151

Row sum: 215 = 32,768 — all subsets of 15 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 15 choose 7?

15 choose 7 is 6,435

Why is 15 choose 7 the same as 15 choose 8?

Every way to choose 7 of 15 items leaves exactly 8 behind, so choosing 7 and choosing which 8 to leave out are the same count: 15 choose 7 = 15 choose 8 = 6,435. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(15, 7) = 32,432,400. Each of the 6,435 combinations can be put in order in 7! = 5,040 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also