Select the correct answerRANI gave her project assignment to a shopkeeper for binding. There were 19 pages including a cover page, 12 pages of theory and 6 pages of drawings. She told the shopkeeper that the theory pages are in a particular order and the drawing pages can be arranged anywhere provided they are together. If the cover page is always kept first what is the probability that rest of the pages are arranged as per requirement?Options13×40/17!13!×6!/18!12𝐶1×6!/18!13𝐶1×6!/19!
Question
Select the correct answerRANI gave her project assignment to a shopkeeper for binding. There were 19 pages including a cover page, 12 pages of theory and 6 pages of drawings. She told the shopkeeper that the theory pages are in a particular order and the drawing pages can be arranged anywhere provided they are together. If the cover page is always kept first what is the probability that rest of the pages are arranged as per requirement?Options13×40/17!13!×6!/18!12𝐶1×6!/18!13𝐶1×6!/19!
Solution
The correct answer is 13𝐶1×6!/19!.
Here's the step-by-step solution:
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The cover page is always first, so we have 18 pages left to arrange.
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The 12 theory pages must be in a specific order, so we treat them as a single item. This gives us 7 items to arrange (the block of theory pages and the 6 drawing pages).
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The drawing pages can be arranged in any order, but they must be together. So, we treat them as a single item as well. This gives us 2 items to arrange (the block of theory pages and the block of drawing pages).
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There are 2! = 2 ways to arrange these 2 items.
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Within the block of drawing pages, there are 6! = 720 ways to arrange the 6 pages.
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So, there are 2 * 720 = 1440 ways to arrange the pages as per the requirement.
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The total number of ways to arrange the 18 pages is 18! = 6402373705728000.
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So, the probability that the pages are arranged as per the requirement is 1440 / 6402373705728000 = 13𝐶1×6!/19!.
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