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?Options12612! / (3! X 3! X 4!)12!12! /(3! X 3! X 4! X 2!)
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?Options12612! / (3! X 3! X 4!)12!12! /(3! X 3! X 4! X 2!)
Solution
The answer to this question can be found using the formula for permutations of multiset: n! / (r1! * r2! * ... * rk!).
Here, n is the total number of items, and r1, r2, ..., rk are the numbers of identical items of each type.
In this case, we have:
- n = 12 (total number of books)
- r1 = 3 (number of identical Quant books)
- r2 = 3 (number of identical Reasoning books)
- r3 = 4 (number of identical English books)
- r4 = 1 (number of one General Awareness book)
- r5 = 1 (number of the other General Awareness book)
So, the number of different ways to arrange these books is:
12! / (3! * 3! * 4! * 1! * 1!)
This simplifies to 12! / (3! * 3! * 4!)
So, the correct option is "12! / (3! X 3! X 4!)".
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