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The number of ways of accomodating 7 guests in 3 rooms so thst no room is empty is


a)1260   b)1440   c)1708   d)1806

3 years ago

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Answers : (1)

                                        

3^7 - 3*2^7 + 3*1^7 = 2187 - 384 + 3 = 1806


 


Inclusion-Exclusion principle.


 


7 guests go into 3 rooms (1 and 2 rooms can be empty) - 7 guests go into 2 rooms (1 and 2 rooms can be empty) + 7 guests go into 1 room (This was excluded twice)

3 years ago

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