SOLUTION: six different statistics books, seven physics books , and 3 different economics books are arranged on a shelf. How many different arrangements are possible if a. the books in eac

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Question 1011934: six different statistics books, seven physics books , and 3 different economics books are arranged on a shelf. How many different arrangements are possible if
a. the books in each particular subject must all stand together
b. only the statistics books must stand together
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There are 6%21=1%2A2%2A3%2A4%2A5%2A6=720 ways to organize the 6 statistics books.
There are 7%21=1%2A2%2A3%2A4%2A5%2A6%2A7=5040 ways to organize the 7 physics books.
There are 3%21=1%2A2%2A3=6 ways to organize the 3 economics books.
There are 3%21=1%2A2%2A3=6 ways to organize the 3 groups of single-subjects books on the self.
So, there are 720%2A5040%2A6%2A6=highlight%28130636800%29 different possible arrangements if the books in each particular subject must all stand together.

There are 6%21=1%2A2%2A3%2A4%2A5%2A6=720 ways to organize the 6 statistics books.
There are 10%21=1%2A2%2A3%2A4%2A5%2A6%2A7%2A8%2A9%2A10=3628800 ways to organize the 7%2B3=10 books on the other subjects.
There are 10%2B1=11 places where the set of statistics books could be inserted together in between the 10 books on the other subjects.
So, there are 720%2A3628800%2A11=highlight%2828740096000%29 different possible arrangements if only the statistics books must stand together.