I want to arrange my books in a self in a certain way. Suppose I have...

I want to arrange my books in a self in a certain way. Suppose I have 30 books (distinct), and of these books, 10 are statistics books, 5 are forest ecology books, 4 are forest genetics, 3 are soil biology and 8 are economics books. I want to keep the books in the same subjects together.

How many ways can I arrange these 30 books?

Hint 1: Books in the same subject are not the same book. For example, ten statistics books here are covering different topics in statistics and written by various authors.

Hint 2: For answering the question use a whole number/integer. For example, the value could be 50000000000000 (this is not the answer)

Solutions

Expert Solution

Total Number of Books = 30

Number of statistics book = 10, number of forest ecology book = 5, number of forest genetics book = 4, number of soil biology book = 3, and number of economics book = 8.

Now, we want to keep the books of the same subject together, and we have books of 5 different subjects. So think them as 5 blocks which can be arranged amongst themselves in 5! = 120 ways.

Stop here for a minute and think that for example, the block of statistics book will have 10 statistic books and in this block, they can be arranged amongst themselves in 10! way. Similarly for other subjects.

So, the total number of ways we can arrange = 5!*10!*5!*4!*3!*8! (10! for 10 statistic book, 5! for forest ecology book, 4! for forest genetics, 3! for soil biology and 8! for economics)

Multiplying the above factorial 5!*10!*5!*4!*3!*8! = 120*3628800*120*24*6*40320 = 303395084697600000.

Please upvote if it helped you :)

orchestra answered 1 year ago

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