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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://gre.myprepclub.com/forum
why did we start with women when men is more restrictive?
Question link: https:/
Question link: https://gre.myprepclub.com/forum/four-women-and-three-men-must-be-seated...
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
Hi brent, when do we use the
The formula you're referring
The formula you're referring to is called the MISSISSIPPI rule, and we use it when we want to arrange a group of items in which some of the items are identical. More on this here: https://www.greenlighttestprep.com/module/gre-counting/video/785
So for example, if we want to arrange 3 identical M's, 2 identical A's and 2 identical H's, then we could do so in 7!/(3!)(2!)(2!) ways.
In the question above, the 3 math books are all different as are the 2 art books and the 2 history books.
For that reason alone, we can't use the Mississippi rule.
In addition, the question has the condition that the math books must be arranged together, as are the art books and history books.
The Mississippi rule doesn't require similar items to be grouped together.