SOLUTION: Suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are different. In how many ways can you put the 30 books in a row on a shelf?

Question 1200908: Suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are different.
In how many ways can you put the 30 books in a row on a shelf?
In how many ways can you get a bunch of four books to give to a friend?
In how many ways can you get a bunch of three history books and seven novels to give to a friend?
In how many ways can you put the 30 books in a row on a shelf if the novels are on the left, the math books are in the middle, and the history books are on the right?
In how many ways can you put the 30 books in a row on a shelf if the five math books are to be grouped together, but there are no restrictions on the placement of the other books?
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!



Suppose you have 30 books (15 novels, 10 history books, and 5 math books). Assume that all 30 books are different.

In how many ways can you put the 30 books in a row on a shelf? 

   30!   (where n! = n*(n-1)*(n-2)*...*3*2*1)



In how many ways can you get a bunch of four books to give to a friend?

   C(30,4)  where  C(n,r) = n!/((n-r)!r!)



In how many ways can you get a bunch of three history books and seven novels to give to a friend?

   C(10,3)*C(15,7)



In how many ways can you put the 30 books in a row on a shelf if the novels are on the left, the math books are in the middle, and the history books are on the right?

    15!*5!*10!



In how many ways can you put the 30 books in a row on a shelf if the five math books are to be grouped together, but there are no restrictions on the placement of the other books? 

  

    Treat the 5 math books as a single unit, temporarily.  This one unit, combined with the remaining 25 books, can be arranged in

       (25+1)! = 26! ways

But for each one of these arrangements, the 5 math books can be arranged in 5! ways, therefore the total  is   

       26!*5!



 

RELATED QUESTIONS

Suppose that you have 3 different math books, 4 different chemistry books, and 5... (answered by stanbon)
In a library the ratio of Sinhalese books to English books is 5:3 if all the English... (answered by KMST)
In how many ways can  you arrange 11 math books and 6 history books if:
a. order matters
 (answered by stanbon)
Suppose the Davao Light and Power Company donated 2500 books to Davao City National High... (answered by ikleyn)
Mia has four math books, three novels and two books of poetry.  She wants to arrange them  (answered by sudhanshu_kmr)
There are 3 math books and 3 history books that are to be arranged on a shelf. How many... (answered by greenestamps,ikleyn)
Three maths books, four science books, two geography books and three history books are to  (answered by ewatrrr)
You have four different history books, three different biology books, and two different... (answered by jorel1380)
On my bookshelf I have 5 books of poetry, 15 graphic novels, 8 biographies and 3... (answered by ikleyn)