17 Choose 5

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

What is 17 choose 5?

Answer

17 choose 5 is
6,188

Order doesn't matter, no repeats: 6,188 ways to choose 5 of 17 items.

C(17, 5) = 17! / (5! · 12!)

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

= 6,188

If order matters (permutations): P(17, 5) = 17 × 16 × 15 × 14 × 13 = 742,560 — each combination in 5! = 120 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 5 for other n

n choose 5Answer
6 choose 56
7 choose 521
8 choose 556
9 choose 5126
10 choose 5252
11 choose 5462
12 choose 5792
13 choose 51,287
14 choose 52,002
15 choose 53,003
16 choose 54,368
17 choose 56,188
18 choose 58,568
19 choose 511,628
20 choose 515,504

FAQ

What is 17 choose 5?

17 choose 5 is 6,188

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

Every way to choose 5 of 17 items leaves exactly 12 behind, so choosing 5 and choosing which 12 to leave out are the same count: 17 choose 5 = 17 choose 12 = 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, 5) = 742,560. Each of the 6,188 combinations can be put in order in 5! = 120 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also