In a performance there will be 5 songs and 3 dances
Total objects 5+3 = 8
Number of ways of arranging this objects is 8! = 40,320...........(1)
If all the dances must be next to each other than all dances should take as an object as 3!
Number of ways of arranging performing taking dance to each other
is = (5+1)! 3!
= 6! 3!
= 4320 ....................(2)
Number of ways to arrange the shows if all dances can not be next to each other = (1) - (2)
= 40320-4320
= 3600 ways
Number of ways to arrange the shows if all the dances must be next to each other is 4320 ways.
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