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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6629
GMAT 1: 760 Q51 V42
GPA: 3.82
A club has 10 members. One president and two vice-presidents are elect  [#permalink]

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28 Nov 2018, 01:09
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:54) correct 25% (00:45) wrong based on 36 sessions

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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 09 Jun 2014 Posts: 218 Location: India Concentration: General Management, Operations Schools: Tuck '19 A club has 10 members. One president and two vice-presidents are elect [#permalink] ### Show Tags 28 Nov 2018, 02:10 2 MathRevolution 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 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!! CEO Joined: 11 Sep 2015 Posts: 3237 Location: Canada Re: A club has 10 members. One president and two vice-presidents are elect [#permalink] ### Show Tags 28 Nov 2018, 06:43 Top Contributor MathRevolution 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- ... /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. RELATED VIDEO FROM OUR COURSE _________________ Test confidently with gmatprepnow.com CEO Joined: 11 Sep 2015 Posts: 3237 Location: Canada Re: A club has 10 members. One president and two vice-presidents are elect [#permalink] ### Show Tags 28 Nov 2018, 06:46 Top Contributor MathRevolution 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- ... /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. RELATED VIDEO FROM OUR COURSE _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6629 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A club has 10 members. One president and two vice-presidents are elect [#permalink] ### Show Tags 30 Nov 2018, 01:18 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: A club has 10 members. One president and two vice-presidents are elect &nbs [#permalink] 30 Nov 2018, 01:18
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