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A club has 10 members. One president and two vice-presidents

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by Max@Math Revolution » Wed Nov 28, 2018 12:20 am

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[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
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by GMATGuruNY » Wed Nov 28, 2018 3:12 am
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.

The correct answer is E.
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by Brent@GMATPrepNow » Wed Nov 28, 2018 6:34 am
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: https://www.gmatprepnow.com/module/gmat- ... /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)

Answer: E
--------------------------

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: https://www.gmatprepnow.com/module/gmat- ... /video/775

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

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
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- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
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- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
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- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Fri Nov 30, 2018 12:44 am
=>

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.

Therefore, the answer is E.
Answer: E
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