Two members of a certain club are selected to speak...

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Two members of a certain club are selected to speak at the next club meeting. If there are 36 different possible selections of the 2 club members, how many members does the club have?

A. 5
B. 6
C. 7
D. 8
E. 9

The OA is E.

Is there a strategic approach to this PS question?

I did it this way.
We know total number of ways of selecting 2 People out of n people is nC2 = 36(given in the question)
$$ie,\ \ n!/(2!*(n-2)!)=[n(n-1)*(n-2)!]/[(2!*(n-2)!)]=n(n-1)/2$$
so n(n-1)/2=36

n(n-1)=72

We know 72 = 9*8

so n=9

Is the approach right ?
Source: — Problem Solving |

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by EconomistGMATTutor » Sat Dec 23, 2017 3:32 am
Hello AAPL.

Your answer is very well.

Another way you could try it is: we have to choose 2 people (the order doesn't matter), we have two places: _____ _____.

For the first place we have n options and for the second place we have n-1 options. So, we have n*(n-1) options. But, we have to divide it by 2 (beacuse the order doesn't matter). That is to say, $$\frac{n\cdot\left(n-1\right)}{2}=36\ \leftrightarrow\ \ n\left(n-1\right)=72\ \leftrightarrow\ n=9.$$ I hope this explanation can help you.

Feel free to ask me again if you have a doubt.

Regards.
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by Scott@TargetTestPrep » Sun Sep 08, 2019 5:49 am
AAPL wrote:Two members of a certain club are selected to speak at the next club meeting. If there are 36 different possible selections of the 2 club members, how many members does the club have?

A. 5
B. 6
C. 7
D. 8
E. 9
Letting n = the number of members in the club, we can create the equation:

nC2 = 36

n! / [2! x (n - 2)!] = 36

n(n - 1)(n - 2)(n - 3)... / [2! (n - 2)(n - 3)..] = 36

(n)(n - 1) / 2! = 36

n^2 - n = 72

n^2 - n - 72 = 0

(n - 9)(n + 8) = 0

n = 9 or n = -8

Since n can't be negative, n = 9.

Answer: E

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AAPL wrote:Two members of a certain club are selected to speak at the next club meeting. If there are 36 different possible selections of the 2 club members, how many members does the club have?

A. 5
B. 6
C. 7
D. 8
E. 9
Let n = TOTAL number of members.

Since the order in which we select the two members does not matter, this is a COMBINATION question.
We can write: nC2 = 36

This means (n)(n-1)/(2)(1) = 36
In other words, (n)(n-1) = 72
We COULD try to solve this equation, but it might be faster to check the answer choices.

A) 5
If n = 5, then we get: (n)(n-1) = (5)(5-1) = 72 NOT TRUE
.
.
.
E) 9
If n = 9, then we get: (n)(n-1) = (9)(9-1) = 72 WORKS!!

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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