BOOKS ARRANGEMENT

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Suppose a student has 3 books and his book-rack has 3 shelves. He has to arrange the books in the shelves. How many ways are there?

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There are 3 cases.

Case I : he puts one book in each shelf:
Total number of case I ways = 3 *2 * 1 = 3! = 6

Case II: he puts 2 books together in one shelf and the remaining 1 book in another shelf.
for arranging 2 books together
Total number of ways = 6

For arranging 2 books into 3 shelves, total number of ways = 3p2 = 3! / (3-2)! = 6

So total number of case II ways = 6 * 6 = 36

case III: he puts all the 3 books together in one shelf.

For arranging 1 books into 3 shelves, total number of ways = 3

Total number of case III ways = 3 * 6 = 18

Thus, case i + case ii + case iii = 6 + 36 + 18 = 60

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