A student has 3 math books, 4 history books, 2 chemistry books, and 1 Latin book
ID: 3205484 • Letter: A
Question
A student has 3 math books, 4 history books, 2 chemistry books, and 1 Latin book. He wants to arrange them on a bookshelf. (Throughout b-e assume all books from a particular topic have the same title)
A. If all the books have different titles, in how many distinct ways can he arrange them?
B. In how many distinct ways can he arrange his books?
C. If he groups the identical math books together, and he groups the identical history books together, and he groups the identical chemistry books together, in how many distinct ways can he arrange his books?
D. If he groups the identical history books together (but isn't picky about the other books), in how many distinct ways can he arrange his books?
E. What is the probability that none of the history books are together?
Explanation / Answer
A) Total number of books = 10
If all have distinct titles, no of arrangements possible = 10!
= 10x9x8x....3x2x1 = 3628800
B) If books from a particular topic have same title, no of arrangements possible = 10!/(3!x4!x2!x1!) = 12600
C) Then there are only 4 set of books that can be arranged in 4! ways = 4x3x2x1 = 24
D) Then its like having 7 books (group of 4 history books can be treated as a large single book) and no of ways possible = 7!/(3!x2!x1!x1!) = 420
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