Consider the 3-lists taken from . How many are there in which each element of  appears at least once?
I get .
Answer the same question, but for 4-lists and 5-lists taken from .
For the 4-list I get *3.
For the 5-list I get * .
Are these answers correct?
The 3-lists would then be 123 132 213 231 312 and 321.
A list is an ordered sequence of objects, and a k-list is a list of length k.
Lists are also called words. Can also be written (1,2,3) etc. Without the constraint that the elements can only appear once, (1,1,1) would also be a 3-list of .
Since every element must appear at least once, for the 3-list the lists would be (1,2,3) (1,3,2) (2,1,3) (2,3,1) (3,1,2) and (3,2,1); without the constraint we could add (1,1,1) (1,1,2) (1,1,3) etc.
Now with this understanding <3,2,1,1> is different from <1,2,3,1>.
If it means that those are not different then the answer in .