GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Nov 2018, 01:46

### GMAT Club Daily Prep

#### 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

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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### GMATbuster's Weekly GMAT Quant Quiz # 9

November 17, 2018

November 17, 2018

09:00 AM PST

11:00 AM PST

Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

# Sixteen children are trying to decide which two children will win the

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50617
Sixteen children are trying to decide which two children will win the  [#permalink]

### Show Tags

31 Jan 2017, 09:11
1
2
00:00

Difficulty:

35% (medium)

Question Stats:

63% (01:13) correct 37% (01:14) wrong based on 209 sessions

### HideShow timer Statistics

Sixteen children are trying to decide which two children will win the president and vice-president positions in the class. Each child can and will cast a vote for anyone in the class. If each child in the class is eligible for a position, how many different outcomes are there of the election?

A. 15
B. 30
C. 60
D. 120
E. 240

_________________
CEO
Joined: 11 Sep 2015
Posts: 3120
Sixteen children are trying to decide which two children will win the  [#permalink]

### Show Tags

31 Jan 2017, 11:52
1
Top Contributor
4
Bunuel wrote:
Sixteen children are trying to decide which two children will win the president and vice-president positions in the class. Each child can and will cast a vote for anyone in the class. If each child in the class is eligible for a position, how many different outcomes are there of the election?

A. 15
B. 30
C. 60
D. 120
E. 240

Take the task of selecting a president and vice-president, and break it into stages.

Stage 1: Select someone to be president.
There are 16 children to choose from, so we can complete stage 1 in 16 ways

Stage 2: Select someone to be vice-president.
Once a child has been selected to be president, that child cannot also be vice-president.
So, there are 15 remaining children to choose from, so we can complete stage 2 in 15 ways

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus select a president and vice-president) in (16)(15) ways (240 ways)

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT so be sure to learn it.

RELATED VIDEOS FROM OUR COURSE

_________________

Brent Hanneson – GMATPrepNow.com

##### General Discussion
Intern
Joined: 17 Nov 2016
Posts: 26
Re: Sixteen children are trying to decide which two children will win the  [#permalink]

### Show Tags

05 Jul 2018, 15:18
Quote:
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus select a president and vice-president) in (16)(15) ways (240 ways)

Why can't we solve it this way? 16c2=120?
Intern
Joined: 08 Apr 2017
Posts: 3
Location: India
WE: Consulting (Real Estate)
Re: Sixteen children are trying to decide which two children will win the  [#permalink]

### Show Tags

08 Jul 2018, 07:44
Imagine there were just 3 students - A, B, C for the post of President and Vice President.
Total no of combinations is AB, BA, AC, CA, BC, CB. i.e 3p2 ways = 6 ways.

Similarly for 16 students, it will be 16p2 = 240 ways
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)
Re: Sixteen children are trying to decide which two children will win the  [#permalink]

### Show Tags

09 Jul 2018, 18:55
Bunuel wrote:
Sixteen children are trying to decide which two children will win the president and vice-president positions in the class. Each child can and will cast a vote for anyone in the class. If each child in the class is eligible for a position, how many different outcomes are there of the election?

A. 15
B. 30
C. 60
D. 120
E. 240

We use permutations because the order is important. For example, the two outcomes (James President and Charlie Vice-President) and (Charlie President and James Vice-President) are different from each other..The number of possible outcomes is 16P2 = 16!/14! = 16 x 15 = 240.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Joined: 31 Aug 2016
Posts: 167
Location: India
Concentration: Finance, General Management
GMAT 1: 680 Q49 V33
GMAT 2: 700 Q49 V37
GPA: 2.81
Re: Sixteen children are trying to decide which two children will win the  [#permalink]

### Show Tags

11 Jul 2018, 00:34
Bunuel wrote:
Sixteen children are trying to decide which two children will win the president and vice-president positions in the class. Each child can and will cast a vote for anyone in the class. If each child in the class is eligible for a position, how many different outcomes are there of the election?

A. 15
B. 30
C. 60
D. 120
E. 240

children no selected/not selected
1 yes
2 yes
3 no
.
.
.
16 no

Out of first two children one can be president and the other can be VP or vice-a-versa
but they are not same

total arrangement = 16!

remove arranement of 14 children not selcted
arrangement of each selected, president = 1!
VP = 1!

answer = $$\frac{16!}{14!*1!*1!}$$ = 16 * 14 = 240
_________________

Resources
GMATNinja Webinars
GMATNinja Chats

Quant
Mixtures

Re: Sixteen children are trying to decide which two children will win the &nbs [#permalink] 11 Jul 2018, 00:34
Display posts from previous: Sort by