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In how many ways can 5 different mathematics books, 4 different physic

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Bunuel
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In how many ways can 5 different mathematics books, 4 different physic [#permalink] New post   03 Mar 2021, 04:00
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In how many ways can 5 different mathematics books, 4 different physics books and 2 different chemistry books be arranged on a shelf if the books in each subject are to be together?

A. 2!*3!*4!*5!
B. 2!*2!*3!*4!
C. 2!*(3! + 4! + 5!)
D. 2! + 3! + 4! + 5!
E. 3! + 4! +5!
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Re: In how many ways can 5 different mathematics books, 4 different physic [#permalink] New post   03 Mar 2021, 04:06
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Take the 5 Math books as 1 unit, 4 Physics books as 1 unit and 2 chemistry books as 1 unit.

Externally, we can arrange these 3 units in 3! ways.

internally, the math books can be arranged in 5! ways, Physics in 4! ways and chemistry books in 2! ways.

Total Arrangements = 3! * 5! * 4! * 2!


Option A

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Re: In how many ways can 5 different mathematics books, 4 different physic [#permalink] New post   03 Mar 2021, 04:17
Bunuel wrote:
In how many ways can 5 different mathematics books, 4 different physics books and 2 different chemistry books be arranged on a shelf if the books in each subject are to be together?

A. 2!*3!*4!*5!
B. 2!*2!*3!*4!
C. 2!*(3! + 4! + 5!)
D. 2! + 3! + 4! + 5!
E. 3! + 4! +5!


Taking 5 different mathematics book as 1 unit, 4 different physics book as 1 unit & 2 different chemistry book as 1 unit, there are total 3 units.
These 3 units can be arranged in 3! ways.

Now, 5 different mathematics book in the 1st unit can be arranged in 5! ways.
4 different physics books in the 2nd unit can be arranged in 4! ways.
2 different chemistry books in the 3rd unit can be arranged in 2! ways.

So, Total number of ways in which the books can be arranged on the shelf = 3!*5!*4!*2! = 2!*3!*4!*5!

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Re: In how many ways can 5 different mathematics books, 4 different physic [#permalink] New post   03 Mar 2021, 06:56
Take each subject as one unit

they can be arranged in 3! ways. In each subject pack, the books can be arranged in n! ways

Total combinations = 3!*5!*4!*2!

Option A is the answer.

Hope this helps
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Re: In how many ways can 5 different mathematics books, 4 different physic [#permalink]
03 Mar 2021, 06:56
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