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28 Nov 2018, 02:09
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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82% (01:19) correct
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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
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
28 Nov 2018, 03:10
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Bookmarks
MathRevolution
There are two ways of doing.
Either you select one president and then select 2 Vice presidents from remaining(that is 10-1=9 remaining) --10*
or
You select 2 vice president and then select 1 president from remaining(that is 10-2= 9 remaining) --10C2*8C1
For first way --
No of ways of selecting one President from 10 = 10C1 = 10 ways
No of ways of selecting two Vice- President from remaining (9) = 9C2
Total number of ways = 10*9C2= 360
So E is the answer.
Press Kudos if it helps!!
28 Nov 2018, 07:43
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MathRevolution
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. So, be sure to learn it.
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