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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A club has 10 members. One president and two vice-presidents tagged by: Max@Math Revolution ##### This topic has 3 expert replies and 0 member replies ### GMAT/MBA Expert ## A club has 10 members. One president and two vice-presidents ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] A club has 10 members. One president and two vice-presidents are elected. In how many ways can they be selected? A. 240 B. 280 C. 300 D. 320 E. 360 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

A club has 10 members. One president and two vice-presidents are elected. In how many ways can they be selected?

A. 240
B. 280
C. 300
D. 320
E. 360
Number of options for president = 10. (Any of the 10 members.)
From the remaining 9 members, the number of ways to choose 2 to serve as vice-president = 9C2 = (9*8)/(2*1) = 36.
To combine these options, we multiply:
10*36 = 360.

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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

A club has 10 members. One president and two vice-presidents are elected. In how many ways can they be selected?

A. 240
B. 280
C. 300
D. 320
E. 360
Take the task of selecting the president and two vice-presidents and break it into stages.

Stage 1: Select the president
There are 10 people to choose from. So, we can complete stage 1 in 10 ways

Stage 2: Select two people to be the vice-presidents
Since the order in which we select the two people does not matter, we can use combinations.
We can select 2 people from the remaining 9 people in 9C2 ways (36 ways)
So, we can complete stage 2 in 36 ways

If anyone is interested, we have a free video on calculating combinations (like 9C2) in your head: http://www.gmatprepnow.com/module/gmat-counting/video/789

By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus select a president and two vice presidents) in (10)(36) ways (= 360 ways)

--------------------------

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting/video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat-counting/video/776

Then you can try solving the following questions:

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- http://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html
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Cheers,
Brent

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The number of ways to choose one president out of 10 people is 10C1 = 10.
The number of ways to choose two vice-presidents out of the remaining 9 people is 9C2 = (9*8)/(1*2) = 36.
Thus, the number of ways to choose one president and two vice-presidents out of 10 people is 10 * 36 = 360.

_________________

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