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## Comment on

Books on a Shelf## Can you clarify this why you

## In the solution, the first

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

## In the lesson for factorials

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 the 7 books could be

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

## If you're referring to the

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

Cheers,

Brent

## https://greprepclub.com/forum

why did we start with women when men is more restrictive?

## Question link: https:/

Question link: https://greprepclub.com/forum/four-women-and-three-men-must-be-seated-in...

Good question!

Even though there's a restriction on the men, that same restriction also applies (indirectly) to the women.

For example, if no 2 men can stand together, that also means that all 4 women can't stand together.

Does that help?

Cheers,

Brent

## Is there a way to identify

## Not really.

Not really.

In most cases, a restriction on one part of the question will spill over into other parts.

Consider this question:

A, B, C, D and E must stand in a row. B must stand in the MIDDLE.

In how many different ways can we arrange all 5 people?

The restriction seems to apply to person B. However, the restriction also places limits on the other people as well, since they cannot stand in the middle position.

If you come across a question in which you're unsure how to deal with a restriction, just let me know, and we'll tackle the question together.

Cheers,

Brent

## Hi Brent, I wanted to tackle

In here we have this _ _ B _ _

Does this mean we cna accomplish this in 4*3*2*1 ways = 24 ways? Thanks

## That's correct, Carla.

That's correct, Carla.

That is, we can seat person B in 1 way (in the middle).

We can seat person A in 4 ways (since there are now 4 chairs remaining)

We can seat person C in 3 ways (since there are now 3 chairs remaining)

We can seat person D in 2 ways (since there are now 2 chairs remaining)

We can seat person E in 1 way (since there's now 1 chair remaining)

So, the total number of ways to seat all five people equals = (1)(4)(3)(2)(1)

= 24

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