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How many different ways can 5 Musicians, 2 Artists, and 3 Guitarists be seated in a row in the auditorium so that every one of the same profession sits together?

Option: 1

1230


Option: 2

1310

 


Option: 3

1440

 


Option: 4

1520


Answers (1)

best_answer

The 5 Musicians can be seated together in 5! ways. 

The 2 Artists can be seated together in 2! Ways.

The 2 Guitarists can be seated together in 3! Ways.

Thus, the different ways can 5 Musicians, 2 Artists, and 3 Guitarists be seated in a row in the auditorium so that every one of the same profession sits together is,

\begin{aligned} & 5 ! \times 2 ! \times 3 !=5 \times 4 \times 3 \times 2 \times 2 \times 3 \times 2 \\ & 5 ! \times 2 ! \times 3 !=1440 \end{aligned}

Therefore, the number of ways is 1440 ways.  

 

  

 

 

 

 

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