17 Choose 6

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

What is 17 choose 6?

Answer

17 choose 6 is
12,376

Order doesn't matter, no repeats: 12,376 ways to choose 6 of 17 items.

C(17, 6) = 17! / (6! · 11!)

= (17 × 16 × 15 × 14 × 13 × 12) / (6 × 5 × 4 × 3 × 2 × 1)
= 8,910,720 / 720

= 12,376

If order matters (permutations): P(17, 6) = 17 × 16 × 15 × 14 × 13 × 12 = 8,910,720 — each combination in 6! = 720 orders.

Row 17 of Pascal's triangle
k17 choose k
01
117
2136
3680
42,380
56,188
612,376
719,448
824,310
924,310
1019,448
1112,376
126,188
132,380
14680
15136
1617
171

Row sum: 217 = 131,072 — all subsets of 17 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 17 choose 6?

17 choose 6 is 12,376

Why is 17 choose 6 the same as 17 choose 11?

Every way to choose 6 of 17 items leaves exactly 11 behind, so choosing 6 and choosing which 11 to leave out are the same count: 17 choose 6 = 17 choose 11 = 12,376. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(17, 6) = 8,910,720. Each of the 12,376 combinations can be put in order in 6! = 720 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also