ShmoopTube

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Here’s your shmoop du jour, brought to you by Bookshelves.

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They’re those antiquated things you can… put your Kindle on.

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Four books, each with different titles, are going to be placed on a shelf.

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Approximately what is the probability that they will be placed in alphabetical order?

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And here are the potential answers…

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No matter how many books we have, there is only one way

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to put them in alphabetical order if they all have different titles.

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So…out of all of the different ways to order these books, only one is a favorable outcome.

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Since probability can be calculated with the formula: favorable over number of possible ways…

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…we only need to figure out the number of possible ways to solve this problem.

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The possible ways we can order 4 books sounds like a permutations problem.

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There are 4 slots in which we can place books.

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In the first slot, there are 4 choices…meaning if we were to randomly choose a book to put there,

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any of the 4 would be fine and dandy. Now, we have 3 left.

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In the second slot, there are 3 to choose from, since we already placed the first one.

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Next, there are 2 to choose from, and then only 1.

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We multiply all of these numbers together to find out the total number of possible permutations.

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When we randomly place books, there are 24 ways to place 4 of them.

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Out of those 24, only 1 is in alphabetical order.

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That comes out to be about to be 1 over 24 or about 4%, so our answer is (B).

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