A probability problem by A Former Brilliant Member
Mr. Lee has different books that he is going to put on his bookshelf. Of these, are biology books, are chemistry books, are logic books, and are pre-calculus books. Mr. Lee wants to arrange his books so that all the books dealing with the same subject are together on the shelf. How many different arrangements are possible?
The answer is 41472.
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1 solution
There are 4 ! 3 ! 2 ! 3 ! arrangements such that the biology books are first in line, then the chemistry books, then the logic books, and then the pre-calculus books. Similarly, for each possible ordering of the subjects, there are 4 ! 3 ! 2 ! 3 ! possible arrangements. Hence, as there are 4! possible orderings of the subjects, the desired answer is 4 ! 4 ! 3 ! 2 ! 3 ! = 4 1 4 7 2 .