Cool combinatorics at your library ;)

Probability Level 2

In how many ways can be three math books, 7 physics books and 5 chemistry books be arranged in a shelf, if the books of each subject must be kept together? (Also, given that books of each subjects are not identical)

The answer is 21772800.

1 solution

Tijmen Veltman
Apr 9, 2015

The three subjects can be arranged in $3!$ ways. For each subject, the books can be arranged in $n!$ ways (where $n$ is the number of books in that subject) giving us

$3! \text{ (three subjects)} \times 3! \text{ (math)}\times 7! \text{ (physics)}\times 5! \text{ (chemistry)} = \boxed{21772800}.$

Cool combinatorics at your library ;)

The answer is 21772800.

1 solution

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