+614 For a New Year's photograph, four dwarves and four elves are supposed to stand in a line such that the dwarves and elves do not mix. However, the elves had a long night of partying and are unable to follow directions. In how many ways can the eight individuals stand in a line such that the dwarves all stand together but the elves do not all stand together?
+526 Total no. of ways = 8!
= 40320
No. of dwarves = 4
No. of elves = 4
Hence, let all dwarves be considered as one object
No. of ways accordingly = 5!
= 120
No. of ways to arrange among themselves = 4!
Thus, required no. of ways = 2880
