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  • the number of ways of allotting three rooms of a hotel among 12 guests, where one room has a capacity of 3, second has a capacity of 4 and third has a capacity of 5 is <div

the number of ways of allotting three rooms of a hotel among 12 guests, where one room has a capacity of 3, second has a capacity of 4 and third has a capacity of 5 is 

Option: 1

12! 


Option: 2

27720


Option: 3

12!.3!.4!.5!


Option: 4

27722


Answers (1)

best_answer

For (m+n+r) distinct objects which have to be grouped into three unequal groups containing m,n and r objects, grouping can be done in

\\\mathrm{\frac{(m+n+r)!}{m!n!r!}} number of ways

 

Now,

Firstly 12 people have to be divided into three groups of 3 , 4 and 5 

No. of ways of grouping = \frac{12 !}{3! 4 ! 5 !}

After division allottment can be done only in one way

Total number of ways = \frac{(12) !}{(3)! (4) ! (5) !}= 27720

Posted by

vishal kumar

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