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Tamil Nadu Board of Secondary EducationHSC Science Class 11

In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together

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Question

In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together

Sum
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Solution

Number of maths book = 4

Number of physics books = 3

Number of chemistry books = 2

Number of biology books = 1

Since we want books of the same subjects together 

We have to treat all maths books as 1 unit 

All physics books as 1 unit

All chemistry books as 1 unit 

And all biology books as 1 unit.

Now the total number of units = 4

They can be arranged in 4! ways.

After this arrangement.

4 maths book can be arranged in 4! ways

3 physics book can be arranged in 3! ways

2 chemistry book can be arranged in 2! ways

And 1 biology book can be arranged in 1! way

∴ Total Number of arrangements 4! 4! 3! 2! = 6912

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Chapter 4: Combinatorics and Mathematical Induction - Exercise 4.2 [Page 178]

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Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 4 Combinatorics and Mathematical Induction
Exercise 4.2 | Q 11 | Page 178

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