Question 930337
(a) With the {{{26}}} letters we use in the USA, we can form 
{{{26*25*24*23=358800}}} different "words" with no repeated letters.
If a list has {{{6*358800=2152800}}} such "words",
it could contain exactly {{{6}}} repeats of each of those "words",
but not have any of them repeated {{{7}}} times.
However, a list with {{{2152800+1=highlight(2152801)}}} such "words"
must have at least of of them repeated {{{7}}} or more times.

(b) If there are {{{2870401}}} "words" on a list of 4-letter sequences made of 4 different letters,
all the {{{2870401}}} "words" could be ABCD, so I would say there is at least (((1))) repeated word.
However, if what the question means to ask is what is the maximum number of repetitions in that list,
{{{2870401/358800=8&1/358800}}} ,
meaning that when you divide,
you get a quotient of {{{8}}} and a remainder of {{{1}}} ,
or in other words {{{2870401=358800*8+1}}} .
That means that to have words repeated as few times as possible,
we need to repeat each of the {{{358800}}} words {{{8}}} times,
and then include an extra repetition of one of those words,
that would be repeated {{{highlight(9)}}} times.
Any list length between {{{2870401=358800*8+1}}} and {{{3229200=358800*9}}}
would have at least {{{9}}} repetitions of one or more words.