9 Choose 6

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

What is 9 choose 6?

Answer

9 choose 6 is
84

Order doesn't matter, no repeats: 84 ways to choose 6 of 9 items.

Choosing 6 of 9 is the same as leaving 3 out: C(9, 6) = C(9, 3).

C(9, 6) = 9! / (6! · 3!)

= C(9, 3)

= (9 × 8 × 7) / (3 × 2 × 1)
= 504 / 6

= 84

If order matters (permutations): P(9, 6) = 9 × 8 × 7 × 6 × 5 × 4 = 60,480 — each combination in 6! = 720 orders.

Row 9 of Pascal's triangle
k9 choose k
01
19
236
384
4126
5126
684
736
89
91

Row sum: 29 = 512 — all subsets of 9 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 9 choose 6?

9 choose 6 is 84

Why is 9 choose 6 the same as 9 choose 3?

Every way to choose 6 of 9 items leaves exactly 3 behind, so choosing 6 and choosing which 3 to leave out are the same count: 9 choose 6 = 9 choose 3 = 84. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(9, 6) = 60,480. Each of the 84 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also