Book arrangements

Probability Level pending

Four algebra books, six geometry books, four physics books and three chemistry books are to be arranged in a bookshelf. The left most must contain four geometry books followed by three physics books and followed by two algebra books. How many arrangements are possible? Assume that all books are distinct.


The answer is 4180377600.

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1 solution

Total number of books = 4+6+4+3=17. The right most must contain 17-9=8 assorted books.

n u m b e r o f w a y s = ( 6 C 4 ) ( 4 ! ) × ( 4 C 3 ) ( 3 ! ) × ( 4 C 2 ) ( 2 ! ) × 8 ! = number~of~ways=(6C4)(4!) \times (4C3)(3!) \times (4C2)(2!) \times 8!= 4180377600 \color{#D61F06}\boxed{4180377600}

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