# eleven books, consisting of five science books, four english books and two language books, are arranged in a deck at random. what is the probability that the books of each kind are all together?

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## Eleven books consisting of 5 Mathematics, 4 Physics and 2 on Chemistry are placed on a shelf at random. Find the number of possible ways of arranging them on the assumption that the books on the same subject are all together.

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## Eleven books consisting of 5 Mathematics, 4 Physics and 2 on Chemistry are placed on a shelf at random. Find the number of possible ways of arranging them on the assumption that the books on the same subject are all together.

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Updated on : 2022-09-05

Here,Solution Verified by Toppr

Total number of books =5+4+2=11

Now,

11 books can be arranged in 11! ways.

Now, if we want to keep same subject's books together, then number of ways of arranging them subject wise =3!

Further,

5 Mathematics books can be arranged in 5! ways

4 Physics books can be arranged in 4! ways

2 Chemistry books can be arranged in 2! ways

Therefore,

Total number of desired event =2!×3!×4!×5!

Therefore,

Required probability =

11! 2!×3!×4!×5!

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## Eleven books, consisting of five Engineering books, four Mathematics books and two Physics books, are arranged in a shelf at random. What is the probability that the books of each kind are all together?

Eleven books, consisting of five Engineering books, four Mathematics books and two Physics books, are arranged in a shelf at random. What is the probability t

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Eleven books, consisting of fi...

Eleven books, consisting of five Engineering books, four Mathematics books and two Physics books, are arranged in a shelf at random. What is the probability that the books of each kind are all together?

Updated On: 27-06-2022

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Text Solution Open Answer in App A 5 1155 51155 B 2 1155 21155 C 3 1155 31155 D 1 1155 11155 Answer

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## There are 11 books, 5 engineering books, 4 math books, and 2 physics books arranged in a shelf at random. What is the probability that books of each kind are all together?

Answer: This question should be in Mathematics section. Anyway, 11 books can be arranged in 11! ways. Now for your required event, if we want to stack books of same subjects together then there are 3! ways of arranging them subject wise. For Example E,P,M or E,M,P or P,E,M or P,M,E or M,E,P or M,...

There are 11 books, 5 engineering books, 4 math books, and 2 physics books arranged in a shelf at random. What is the probability that books of each kind are all together?

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Sort Arijit Chatterjee

Avid reader. Lover of Historical and Science Fiction.7y

Originally Answered: Eleven books, consisting of 5 engineering books, 4 maths books, 2 physics books are arranged in a shelf at random .what is the probability that books of each kind are all together?

This question should be in Mathematics section. Anyway, 11 books can be arranged in 11! ways. Now for your required event, if we want to stack books of same subjects together then there are 3! ways of arranging them subject wise.

For Example E,P,M or E,M,P or P,E,M or P,M,E or M,E,P or M,P,E.

Further 5 Engineering books can be arranged in 5! ways, 4 maths books in 4! ways and 2 physics books in 2! ways amongst themselves.

Like this way (E1,E2,E3,E4,E5) (P1,P2) (M1,M2,M3,M4) and similar other ways.

So total ways by which we can get the desired event are 2!*3!*4!*5!.

So probability becomes Probability = No of desired events / Total no. of events.

Probability = (2!*3!*4!*5!)/11!

If there is any mistake in the answer or you still have doubts feel free to comment.

18.7K viewsView upvotes

Bruce Alan Martin

My fascination with numbers began long before I could count.Author has 1.6K answers and 4.8M answer views4y

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In how many ways 4 books of maths and 3 books of physics are placed on shelf that same subject books are always together?

Originally Answered: In how many ways can 4 books of maths and 3 books of physics be placed on a shelf so all books of the same subject books are together?

In how many ways can 4 books of maths and 3 books of physics be placed on a shelf so all books of the same subject books are together?

Since the subjects must be together, there must be all of the math books must be on one end of the shelf and all of the physics book on the other end. Therefore, there are only two arrangements of the subjects: 4 math followed by 3 physics OR 3 physics followed by 4 math.

Within each subject, the number of permutations is

4! = 4*3*2*1 = 24 for the physics books

3! = 3*2*1 = 6 for the physics books

Thus, the number of possible ways to place the books is: 2 * 24 * 6 =

Avik Paul

MSc in Physics, Indian Institute of Technology, Guwahati (IITG) (Graduated 2016)Author has 240 answers and 198.8K answer views3y

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There are 5 books on Mathematics and 4 on Physics. In how many ways can these be placed on a shelf if the books on the same subject are to be together?

Answer : 2! × 5! × 4! = 5760.

5 Mathematics books can be considered as 1 unit and 4 Physics books can be considered as 1 unit. These 2 units can be placed in 2! way. Again 5 Mathematics books can be placed in 5! ways among themselves and 4 Physics books can be placed in 4! ways among themselves. So, you can put the (5+4 =) 9 books in 2! × 5! × 4! = 5760 ways.

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John P. Keller Knows English3y Related

What are the best calculus books?

The problem with books like Thomas’ Calculus or Stewart Calculus is that you won’t get a thorough understanding of the inner mechanics of calculus. As long as you don’t have a good prof or teacher, I would stay away from these books. If you want to understand what I mean, take a look at some arbitrary sections in these books. You’ll see a short paragraph, which serves as an intro, then some boxes with formulas, then a few workout examples and then a bunch of exercises. This means, you will only learn HOW to you the formulas instead of understanding the WHY!

My advice is, visit YouTube, search f

Anthony Clohesy

Maths Graduate, High School Maths teacherAuthor has 159 answers and 1.1M answer views2y

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Suppose you have 40 different books (20 mathematics, 15 physics, and 5 chemistry) and you pick two books at random, one at a time. What is the probability that two books are from different disciplines?

There are lots of ways they can be from different disciplines (MP, PM, PC, CP, MC, CM) but only 3 ways for them to be the same, so I'll work that out and subtract from one:

MM: 20/40 x 19/39 PP: 15/40 x 14/39 CC: 5/40 x 4/39

Added, to get the overall probability of the same type of book:

610/1560 = 61/156

That leaves a 95/156 chance that the two books are different types. (About 61%).

Tahira Khaanam

School TeacherMar 16

Related

4 identical math books and 3 identical physics books are placed in a row. How many different arrangements are possible?

Here, total objects are 7

So, the permutation will be 7!

As, 4 objects are Identical, these books will reduce the permutations and so permutations will be 7!/4!

Again, 3 books are identical, so permutations = 7!/(4!*3!) = 35

Still if you have any doubts, ask me.

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