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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?

 Mar 11, 2021
 #1
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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

 Mar 11, 2021

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