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

 It is currently 19 Jan 2019, 15:02

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 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.

# In how many ways can 3 people out of 14 people be given 3

Author Message
TAGS:

### Hide Tags

Intern
Joined: 16 Jul 2012
Posts: 10
Location: India
GMAT 1: 690 Q44 V40
GPA: 3.6
WE: Design (Telecommunications)
In how many ways can 3 people out of 14 people be given 3  [#permalink]

### Show Tags

Updated on: 07 Nov 2012, 05:55
1
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 11 sessions

### HideShow timer Statistics

In how many ways can 3 people out of 14 people be given 3 prizes(gold,silver,bronze) so that Jack is awarded? Jack is one of 14 people.

468

but I have not been able to understand how.

The direction that I proceeded was:
Jack gets gold or jack gets silver or jack gets bronze
=$$13*12 + 13*12 + 13*12$$

This seems to be wrong,so if somebody could explain where I'm going wrong and how to arrive at the correct answer it would be great!

_________________

Cheers
Vandy
My debrief- For people out of touch with exams http://gmatclub.com/forum/my-gmat-story-690-12-27-q-44-v-40-from-390-q-21-v-144885.html
My blog -http://vandyuncensored.blogspot.in/2012/12/my-gmat-story-690-1227-q-44-v-40-from.html

Originally posted by VandyonWheels on 07 Nov 2012, 05:53.
Last edited by Bunuel on 07 Nov 2012, 05:55, edited 1 time in total.
Renamed the topic.
Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: In how many ways can 3 people out of 14 people be given 3  [#permalink]

### Show Tags

07 Nov 2012, 06:03
In how many ways can 3 people out of 14 people be given 3 prizes(gold,silver,bronze) so that Jack is awarded? Jack is one of 14 people.

The number of groups of 3 to receive prizes is $$C^2_{13}=78$$.

Each of these groups of 3 can be arranged in 3!=6 ways, thus the total ways is 78*6=468.

_________________
Intern
Joined: 24 Apr 2011
Posts: 12
Location: United States
GMAT 1: 710 Q49 V39
GPA: 3.67
Re: In how many ways can 3 people out of 14 people be given 3  [#permalink]

### Show Tags

07 Nov 2012, 06:10
Brunel,

I'm having difficulty understanding why you multiply by 3! Instead
Of simply 3.

Thank you.

Posted from my mobile device
Intern
Joined: 24 Apr 2011
Posts: 12
Location: United States
GMAT 1: 710 Q49 V39
GPA: 3.67
Re: In how many ways can 3 people out of 14 people be given 3  [#permalink]

### Show Tags

07 Nov 2012, 06:20
Actually, I arrived at
The answer a different way. I used
The permutation formula 13!\11! To get 156, and then multiples by 3 for the 3 different ways jack could place.

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: In how many ways can 3 people out of 14 people be given 3  [#permalink]

### Show Tags

07 Nov 2012, 06:22
aceon wrote:
Brunel,

I'm having difficulty understanding why you multiply by 3! Instead
Of simply 3.

Thank you.

Posted from my mobile device

Say one particular group is Jack, X and Y. Now, JXY can be arranged in 3! ways to receive gold, silver, or bronze:

GSB:
JXY
JYX
XJY
XYJ
YJX
YXJ

Hope it's clear.
_________________
Senior Manager
Joined: 13 Aug 2012
Posts: 426
Concentration: Marketing, Finance
GPA: 3.23
Re: In how many ways can 3 people out of 14 people be given 3  [#permalink]

### Show Tags

27 Dec 2012, 21:02
1
My approach:

Since I know that Jack is awarded and another 2 so I have: J _ _

How many ways to select 2 from the remaining 13? 13!/2!1! = 78 Thus, this means there are 78 possible selection of winners from the 14. All of which includes Jack and some other 2 persons.

How many ways to award a group? We can imagine ranking three people as first, second and third. Thus we can get the possible arrangements of 3 people. 3! = 6

78*6 = 468
_________________

Impossible is nothing to God.

Intern
Joined: 12 Jun 2016
Posts: 15
Re: In how many ways can 3 people out of 14 people be given 3  [#permalink]

### Show Tags

07 Aug 2016, 20:39
Hey! I tried an alternate approach where the no. Of ways of choosing prize winners is 1*13*12 and no of permutations is 3! So my answer is 3!*1*13*12
Where am I going wrong here though

Posted from my mobile device
Manager
Joined: 24 Dec 2016
Posts: 96
Location: India
Concentration: Finance, General Management
WE: Information Technology (Computer Software)
In how many ways can 3 people out of 14 people be given 3  [#permalink]

### Show Tags

22 Mar 2017, 19:48
VandyonWheels wrote:
In how many ways can 3 people out of 14 people be given 3 prizes(gold,silver,bronze) so that Jack is awarded? Jack is one of 14 people.

468

but I have not been able to understand how.

The direction that I proceeded was:
Jack gets gold or jack gets silver or jack gets bronze
=$$13*12 + 13*12 + 13*12$$

This seems to be wrong,so if somebody could explain where I'm going wrong and how to arrive at the correct answer it would be great!

Lets ensure Jack gets a prize - 1C1
Choose any 2 from the remaining 13 get prizes - 13C2

Ways of distributing 3 prizes among 3 people - 3!

So total number of ways - $$1C1 * 13C2 * 3!$$ = $$1*13*6*6$$ = $$468$$
In how many ways can 3 people out of 14 people be given 3 &nbs [#permalink] 22 Mar 2017, 19:48
Display posts from previous: Sort by