SOLUTION: a traveling book salesperson has 5 copies of a certain statistic book, 4 copies of a certain geometry book and 3 copies of a certain calculus book. If these books are to be stored
Algebra ->
Permutations
-> SOLUTION: a traveling book salesperson has 5 copies of a certain statistic book, 4 copies of a certain geometry book and 3 copies of a certain calculus book. If these books are to be stored
Log On
Question 1044235: a traveling book salesperson has 5 copies of a certain statistic book, 4 copies of a certain geometry book and 3 copies of a certain calculus book. If these books are to be stored on a shelf in the sales person's van, how many distinct arrangements are possible? Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
a traveling book salesperson has 5 copies of a certain statistic book, 4 copies of a certain geometry book
and 3 copies of a certain calculus book. If these books are to be stored on a shelf in the sales person's van,
how many distinct arrangements are possible?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Had all the book be distinguishable, we would have (5+4+3)! = 12! possible permutations = arrangements of the 12 books.
But for any given arrangement all other 5! arrangements that are differ by permutations of 5 copies of statistical books only,
are actually considered as the same arrangement. We can not make a distinguish between such arrangements.
Therefore, we divide 12! by 5!.
Same with geometry books and the calculus book.
So, the final answer is: there are only = 27720 arrangements.
