Question: Books on a Shelf

Comment on Books on a Shelf

Can you clarify this why you multiply arrange subjects in this math problem? I can't understand this part!
greenlight-admin's picture

In the solution, the first step is to select the order in which the SUBJECT blocks appear.
There are 6 ways to do this:
Math - Art - History
Math - History - Art
History - Art - Math
History - Math - Art
Art - History - Math
Art - Math - History

If we don't include this step, then we aren't account for the 6 possibilities above.

My issue is why are we now using factorals on each arrangement. If you said there were 3 ways to arrange the maths books,2 ways to arrange the history, etc, I would understand. But I dont understand why it is 3!. doesnt that mean 3x2x1?
greenlight-admin's picture

In the lesson for factorials (https://www.greenlighttestprep.com/module/gre-counting/video/780), we learned that we can arrange n unique objects in n! ways.

So, for example, we can arrange the 3 math books in 3! ways.
Likewise, we can arrange the 2 art books in 2! ways.
etc.

Does that help?

It does now! Thank you.

How would the result change if we didn't have to group the books according to subjects?
greenlight-admin's picture

If the 7 books could be arranged in any order, then we could accomplish this task in 7! ways.

Why we didnt use the counting principle here?
greenlight-admin's picture

If you're referring to the video question above, we did use the Fundamental Counting Principle (FCP) to solve this question.

Cheers,
Brent

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