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 (, 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.

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.


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