A set of 12 books has 3 identical Quant books, 3 identical Reasoning books, 4 identical English books and 2 different books on General Awareness. In how many different ways can these 12 books be arranged in a book-shelf?
Question
A set of 12 books has 3 identical Quant books, 3 identical Reasoning books, 4 identical English books and 2 different books on General Awareness. In how many different ways can these 12 books be arranged in a book-shelf?
Solution
This is a permutation problem involving identical objects. The formula for permutations of n objects where there are n1 identical of one type, n2 identical of another type, etc. is:
n! / (n1! * n2! * ...)
In this case, we have:
- 3 identical Quant books
- 3 identical Reasoning books
- 4 identical English books
- 2 different General Awareness books
So, n = 12 (total number of books), n1 = 3 (Quant books), n2 = 3 (Reasoning books), n3 = 4 (English books), and n4 = 2 (General Awareness books).
Substituting these values into the formula, we get:
12! / (3! * 3! * 4! * 2!)
Calculating the factorials, we get:
479001600 / (6 * 6 * 24 * 2) = 1663200
So, there are 1,663,200 different ways to arrange these 12 books on a bookshelf.
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