17 Choose 11

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

What is 17 choose 11?

Answer

17 choose 11 is
12,376

Order doesn't matter, no repeats: 12,376 ways to choose 11 of 17 items.

Choosing 11 of 17 is the same as leaving 6 out: C(17, 11) = C(17, 6).

C(17, 11) = 17! / (11! · 6!)

= C(17, 6)

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

= 12,376

If order matters (permutations): P(17, 11) = 17 × 16 × 15 × … × 7 = 494,010,316,800 — each combination in 11! = 39,916,800 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 11 for other n

n choose 11Answer
11 choose 111
12 choose 1112
13 choose 1178
14 choose 11364
15 choose 111,365
16 choose 114,368
17 choose 1112,376
18 choose 1131,824
19 choose 1175,582
20 choose 11167,960

FAQ

What is 17 choose 11?

17 choose 11 is 12,376

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

Every way to choose 11 of 17 items leaves exactly 6 behind, so choosing 11 and choosing which 6 to leave out are the same count: 17 choose 11 = 17 choose 6 = 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, 11) = 494,010,316,800. Each of the 12,376 combinations can be put in order in 11! = 39,916,800 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also