Question 828365
I agree with your solution.
{{{7!/(4!3!)=35}}} is the number of ways Lisa can pick her 3 days,
or the number of ways Mark can pick his 4 days.
The result is the same. There are 35 different ways of doing it, and it does not matter who gets to choose.
 
The hint is misleading. The way I see it, there is no repetition.
Lisa is choosing a set of 3 different days out of the 7 days in a week.
If order mattered, she would get {{{7*6*5=7!/4!}}} ordered lists of 3 days,
but since the same 3 days picked in different order are the same set of 3 days
we divide by the number of ways that each set can be ordered, which is {{{3*2=3!}}}