17 Choose 17

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

What is 17 choose 17?

Answer

17 choose 17 is
1

Order doesn't matter, no repeats: 1 way to choose 17 of 17 items.

There is exactly one way: take all.

C(17, 17) = 17! / (17! · 0!)

= 1

0! = 1 (an empty product), so 17! cancels out completely.

If order matters (permutations): P(17, 17) = 17 × 16 × 15 × … × 1 = 355,687,428,096,000 — each combination in 17! = 355,687,428,096,000 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 17 for other n

n choose 17Answer
17 choose 171
18 choose 1718
19 choose 17171
20 choose 171,140

FAQ

What is 17 choose 17?

17 choose 17 is 1

Why is 17 choose 17 the same as 17 choose 0?

Every way to choose 17 of 17 items leaves exactly 0 behind, so choosing 17 and choosing which 0 to leave out are the same count: 17 choose 17 = 17 choose 0 = 1. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(17, 17) = 355,687,428,096,000. The only combination — all 17 items — can be put in order in 17! = 355,687,428,096,000 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also