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!
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