17 Choose 17

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What is 17 choose 17?

Answer

17 choose 17 is

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
k	17 choose k
0	1
1	17
2	136
3	680
4	2,380
5	6,188
6	12,376
7	19,448
8	24,310
9	24,310
10	19,448
11	12,376
12	6,188
13	2,380
14	680
15	136
16	17
17	1

Row sum: 2¹⁷ = 131,072 — all subsets of 17 items.

Found an error in the calculation or the information?

n choose 17 for other n

n choose 17	Answer
17 choose 17	1
18 choose 17	18
19 choose 17	171
20 choose 17	1,140

Recalculate with different values ↑

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)!.

17 Choose 17

What is 17 choose 17?

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n choose 17 for other n

FAQ

What is 17 choose 17?

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

How many ways are there if order matters?

See Also