Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
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
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.
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
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.
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
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.
Re: A club has 10 members. One president and two vice-presidents are elect
[#permalink]
Show Tags
30 Nov 2018, 02:18
=>
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 = \(\frac{(9*8)}{(1*2)} = 36.\) 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
_________________