[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
A club has 10 members. One president and two vice-presidents
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- Max@Math Revolution
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Number of options for president = 10. (Any of the 10 members.)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
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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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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- Brent@GMATPrepNow
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Take the task of selecting the president and two vice-presidents and break it into stages.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
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
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- 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
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html
Cheers,
Brent
- Max@Math Revolution
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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.
Therefore, the answer is E.
Answer: E
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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