17 Choose 12

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

What is 17 choose 12?

Answer

17 choose 12 is
6,188

Order doesn't matter, no repeats: 6,188 ways to choose 12 of 17 items.

Choosing 12 of 17 is the same as leaving 5 out: C(17, 12) = C(17, 5).

C(17, 12) = 17! / (12! · 5!)

= C(17, 5)

= (17 × 16 × 15 × 14 × 13) / (5 × 4 × 3 × 2 × 1)
= 742,560 / 120

= 6,188

If order matters (permutations): P(17, 12) = 17 × 16 × 15 × … × 6 = 2,964,061,900,800 — each combination in 12! = 479,001,600 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 12 for other n

n choose 12Answer
12 choose 121
13 choose 1213
14 choose 1291
15 choose 12455
16 choose 121,820
17 choose 126,188
18 choose 1218,564
19 choose 1250,388
20 choose 12125,970

FAQ

What is 17 choose 12?

17 choose 12 is 6,188

Why is 17 choose 12 the same as 17 choose 5?

Every way to choose 12 of 17 items leaves exactly 5 behind, so choosing 12 and choosing which 5 to leave out are the same count: 17 choose 12 = 17 choose 5 = 6,188. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(17, 12) = 2,964,061,900,800. Each of the 6,188 combinations can be put in order in 12! = 479,001,600 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also