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Eleven books consisting of 5 Mathematics, 4 Physics and 2 on C

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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.

Name: Video solution 1: 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.
Uploaded: 2024-02-12T13:22:43.000Z
Duration: 6 min
Description: Video solution 1: 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: Feb 12, 2024

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Theodore Discussed

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.

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Here,
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! \times 3! \times 4! \times 5!

Therefore,
Required probability

= \frac{2 ! \times 3 ! \times 4 ! \times 5 !}{11 !}

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Question Text	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.
Updated On	Feb 12, 2024
Topic	Permutations and Combinations
Subject	Mathematics
Class	Class 11
Answer Type	Text solution:1 Video solution: 2
Upvotes	272
Avg. Video Duration	4 min

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.

Text solutionVerified

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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.

Text solutionVerified

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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.