Book arrangements

Probability Level pending

Marvin has 5 Algebra books, 1 Physics book, 5 Geometry books and 3 Chemistry books. He wants to arrange the books on a shelf. The leftmost must be 3 Algebra books followed by 4 Geometry books and the rightmost must be 2 Chemistry books.

In how many ways can he arrange his books?

Assume that all the books in any given subject are distinct from one another.


The answer is 5184000.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

t o t a l total n u m b e r number o f of b o o k s books = = 14 14

n u m b e r number o f of a r r a n g e m e n t s arrangements = = ( 5 C 3 ) ( 3 ! ) ( 5 C 4 ) ( 4 ! ) ( 3 C 2 ) ( 2 ! ) ( 5 ! ) = 5184000 (5C3)(3!)(5C4)(4!)(3C2)(2!)(5!)=5184000

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He can arrange his books in ( 5 C 3 ) ( 3 ! ) ( 5 C 4 ) ( 4 ! ) ( 5 ! ) ( 3 C 2 ) ( 2 ! ) = 5184000 (_5C_3)(3!)(_5C_4)(4!)(5!)(_3C_2)(2!)=5184000 ways.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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