there will be 5 songs and 3 dances in a performance how many distinguished way to arrange the shows if all dances cannot be next to each other? and how many ways to arrange the shows if all dances must be next to each other?



Answer :

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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