Combinatorics!
Probability
Level
4
In how many ways can you distribute 3 identical math books and 3 identical physics books to 3 children if all children get at least 1 book?
The answer is 55.
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1 solution
The boos can be distributed as per following three rules :-
(1) ( 1 , 1 , 4 ) (2) ( 1 , 2 , 3 ) (3) ( 2 , 2 , 2 )
In case 1 : The book combination can be M ,P , MPPP or M , P , MMPP or P,P, MMMP
Total number of ways of distribution is : ( 3 ! / 2 ! + 3 ! + 3 ! / 2 ! ) = 1 2
In case 2 : The book distribution can be M , M ,PPP or M , MP, MPP or M, PP, MMP
and it is same for P , M ,MPP or P , MP, MMP or P, PP, MMM
Each of these combinations will give 3 ! × 6 = 3 6
In case 3: The book distribution can be MM,PP,MP which gives 3 ! = 6 ways
and MP,MP,MP it gives 1 way
So total no of ways of distribution is = 1 2 + 6 + 1 + 3 6 = 5 5