# Lesson: Counting Strategies - Part II

## Comment on Counting Strategies - Part II

### Dear sir,

Dear sir,
I m trying to solve all the reinforcement activities. Apart from these from where I should practice the Gre level questions. (Especially counting and data interpretation) Kindly suggest.
Regards

### GRE Prep Club is an excellent

GRE Prep Club is an excellent source of all GRE questions (official questions and unofficial questions).

Just use their question filter (here https://gre.myprepclub.com/forum/viewforumtags.php) to filter your questions by question type.

Cheers,
Brent

### Thanks for the help.

Thanks for the help.

### Hi, I had difficulty solving

Hi, I had difficulty solving this question: https://gre.myprepclub.com/forum/tricky-there-are-n-teams-playing-in-a-basketball-tournam-11153.html. I still couldn't solve it after looking at the solution.

What is the approach in solving this question?

Thanks,
Manmeet

### This is a crazy hard question

This is a crazy hard question.
Here's my full solution: https://gre.myprepclub.com/forum/tricky-there-are-n-teams-playing-in-a-b...

Cheers,
Brent

### Hi Brent,

Hi Brent,

In the Magoosh sample problem with the 7 points on a circle and creating triangles from the points, how is the fact that three verticies next to each other will not form a triangle? Does 7C3 account for that?

But 3 adjacent points WILL form a triangle.
You may be thinking of counting questions that are set up similarly, but ask you to count the number of DIAGONALS (not triangles).
When counting diagonals, we must recognize that connecting one vertex to an adjacent vertex will not create a diagonal.

Does that help?

Cheers,
Brent

### Ahh yes, that's what I was

Ahh yes, that's what I was thinking. Can you go through the diagonals question again? I've seen it somewhere, but cannot find it. Thanks Brent!

### Here are two questions that

Here are two questions that cover that concept:

Cheers,
Brent

### https://gre.myprepclub.com/forum

Hi,
In step3, how did you arrive at the expression for the no. of games won: n * (n-1)(n-9)

I believe you're referring to pranab01's solution (my solution doesn't involve the variable n).

I'm not sure how pranab01 got that algebraic expression.
It should just be (n-1)(n-9) [note (n)(n-1)(n-9)]
If we continue with pranab01's solution, we see that the n mysteriously disappears!!

Here's my full solution: https://gre.myprepclub.com/forum/tricky-there-are-n-teams-playing-in-a-b...

Cheers,
Brent

### Hi Dear please can you solve

Hi Dear please can you solve this

For an 8-a-side football match, a coach has to choose the team from a squad of 12 boys. Only three of them can play as a goalkeeper and these three cannot play any other position. The other boys can play all the other positions - defense, midfield and forward. If the team should have 1 goal keeper, 3 defenders, 3 midfielders and 1 forward, in how many ways can the coach select the team?

a. 495
b. 108
c. 544320
d. 12580
e. 15120

### One of the reinforcement

One of the reinforcement questions is, "Of a group of 10 PTA members, a committee will be selected that has 1 president and 3 other members. How many different committees could be selected?"

The "1 president and 3 other members" is confusing, so this is written a little strangely and I would have advocated for it to be thrown out. I treated this question as purely FCP...10 x 9 x 8 x 7. You can see how easily confused this can get. It should have said, "1 president AND HIS COMMITTEE OF 3 MEMBERS." That way, we know that we can use the combinations rule for the 3 members. As the problem stands as written, you can easily treat those 3 members as stand-alones (hence, FCP only). See what I mean?

The question reads as follows: Of a group of 10 PTA members, a committee will be selected that has 1 president and 3 other members. How many different committees could be selected?
I don't see the ambiguity here. We need a 4-person committee, and one of those people will be president.
This is an official GRE question, and the test-makers spend a lot of time and money ensuring about their questions are clear and free of ambiguity.

### Have to avoid those 160 to

Have to avoid those 160 to 170 difficulty questions, sorry. Way too excessive in difficulty and not GRE-style questions. I would love to see more 160 to 170 level questions that are directly from GRE sources, like the big book or official guide. The bad thing is that I think only 7 combination/counting questions were in the official guide (I read that somewhere within your site). Thankfully, only 1 or 2 counting questions are likely to be on the GRE anyway. They are worth skipping if too complex.

### Yes, it would be great if

Yes, it would be great if there were more official counting and probability questions.

Please keep in mind that, just because a question was too difficult for you to answer does not necessarily mean it's too difficult to be an official GRE question.
While I may include links to questions that hover in the 168-170 range, I only do so if the question meets the test-makers' strict standards.
Trust me, there are TONS of awful/unrepresentative GRE questions out there.

### https://gre.myprepclub.com/forum

https://gre.myprepclub.com/forum/for-an-8-a-side-football-match-a-coach-has-to-choose-11762.html

For this question , i understand the way in which you break the problem into stages . But apart from goal keeper rest all are alike . Why cant we use 3C1 (Goaljeeper)* 9C7 (rest others) to calculate

9C7 tells us the number of ways to select 7 players from 9 players, but this approach doesn't assign a position to any of the players.