Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 20 Jul 2019, 15:28

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

A man wants to visit at least two of the four cities A, B, C

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 03 Jan 2014
Posts: 48
Concentration: General Management
Schools: Schulich '16
GMAT 1: 690 Q49 V34
A man wants to visit at least two of the four cities A, B, C  [#permalink]

Show Tags

New post Updated on: 02 Feb 2014, 02:35
10
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

46% (01:30) correct 54% (01:28) wrong based on 310 sessions

HideShow timer Statistics


A man wants to visit at least two of the four cities A, B, C and D. How many travel itineraries can he make? All cities are connected to one another.

(A) 24
(B) 6
(C) 60
(D) 12
(E) None of the above

Originally posted by vimal096 on 01 Feb 2014, 22:33.
Last edited by Bunuel on 02 Feb 2014, 02:35, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56304
Re: A man wants to visit at least two of the four cities A, B, C  [#permalink]

Show Tags

New post 02 Feb 2014, 02:40
4
5
vimal096 wrote:
A man wants to visit at least two of the four cities A, B, C and D. How many travel itineraries can he make? All cities are connected to one another.

(A) 24
(B) 6
(C) 60
(D) 12
(E) None of the above


The # of ways to visit 2 cities when order matters = \(P^2_4=\frac{4!}{(4-2)!}=12\): AB, BA, AC, CA, AD, DA, BC, CB, BD, DB. CD, DC.

The # of ways to visit 3 cities when order matters = \(P^3_4=\frac{4!}{(4-3)!}=24\): ABC, ACB, BAC, BCA, CAB, CBA, ...

The # of ways to visit 4 cities when order matters = \(P^4_4=\frac{4!}{(4-4)!}=24\): ABCD, ABDC, ADCD, ...

12 + 24 + 24 = 60.

Answer: C.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 2, 3, 5, 7 and 10. Thank you.
_________________
General Discussion
Senior Manager
Senior Manager
avatar
B
Joined: 17 Sep 2013
Posts: 329
Concentration: Strategy, General Management
GMAT 1: 730 Q51 V38
WE: Analyst (Consulting)
GMAT ToolKit User Reviews Badge
Re: A man wants to visit at least two of the four cities A, B, C  [#permalink]

Show Tags

New post 22 Apr 2014, 10:43
2
We can also say:

4C2*2! + 4C3*3! + 4C4*4!

I am quite confused with this P n C terminologies..on where to use...so I go intutively..i.e First select the elements and then shuffle them with factorial (If required)...Veritas has an excellent guide on combinatorics..which combined with Bunuels Q bank is enough for 700+ Q on this topic
_________________
Appreciate the efforts...KUDOS for all
Don't let an extra chromosome get you down..:P
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56304
Re: A man wants to visit at least two of the four cities A, B, C  [#permalink]

Show Tags

New post 22 Apr 2014, 11:01
1
JusTLucK04 wrote:
We can also say:

4C2*2! + 4C3*3! + 4C4*4!

I am quite confused with this P n C terminologies..on where to use...so I go intutively..i.e First select the elements and then shuffle them with factorial (If required)...Veritas has an excellent guide on combinatorics..which combined with Bunuels Q bank is enough for 700+ Q on this topic


This is correct. \(C^2_4*2!\) is the same as \(P^2_4\).
_________________
Manager
Manager
avatar
Joined: 26 Apr 2015
Posts: 124
Re: A man wants to visit at least two of the four cities A, B, C  [#permalink]

Show Tags

New post 20 Aug 2015, 23:04
Bunuel wrote:
vimal096 wrote:
A man wants to visit at least two of the four cities A, B, C and D. How many travel itineraries can he make? All cities are connected to one another.

(A) 24
(B) 6
(C) 60
(D) 12
(E) None of the above


The # of ways to visit 2 cities when order matters = \(P^2_4=\frac{4!}{(4-2)!}=12\): AB, BA, AC, CA, AD, DA, BC, CB, BD, DB. CD, DC.

The # of ways to visit 3 cities when order matters = \(P^3_4=\frac{4!}{(4-3)!}=24\): ABC, ACB, BAC, BCA, CAB, CBA, ...

The # of ways to visit 4 cities when order matters = \(P^4_4=\frac{4!}{(4-4)!}=24\): ABCD, ABDC, ADCD, ...

12 + 24 + 24 = 60.

Answer: C.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 2, 3, 5, 7 and 10. Thank you.



Why not 4C2x4C3x4C4?
Manager
Manager
User avatar
Joined: 10 Jun 2015
Posts: 117
Re: A man wants to visit at least two of the four cities A, B, C  [#permalink]

Show Tags

New post 20 Aug 2015, 23:42
vimal096 wrote:
A man wants to visit at least two of the four cities A, B, C and D. How many travel itineraries can he make? All cities are connected to one another.

(A) 24
(B) 6
(C) 60
(D) 12
(E) None of the above


At least 2 means 2 or more
2 cities can be selected from 4 in 4C2 ways and these two cities, say, A and B have two distinct itineraries AB and BA
That can be done in 4C2*2! or 4P2 ways=12
Similarly, 3 cities in 4C3*3! or 4P3 ways=24; 4 cities in 4C4*4! or 4P4 ways=24
Total 12+24+24=60 ways.
The correct option is C
Intern
Intern
avatar
Joined: 28 Dec 2015
Posts: 39
Re: A man wants to visit at least two of the four cities A, B, C  [#permalink]

Show Tags

New post 21 Jul 2016, 03:59
SonofAnarchy wrote:
Bunuel wrote:
vimal096 wrote:
A man wants to visit at least two of the four cities A, B, C and D. How many travel itineraries can he make? All cities are connected to one another.

(A) 24
(B) 6
(C) 60
(D) 12
(E) None of the above


The # of ways to visit 2 cities when order matters = \(P^2_4=\frac{4!}{(4-2)!}=12\): AB, BA, AC, CA, AD, DA, BC, CB, BD, DB. CD, DC.

The # of ways to visit 3 cities when order matters = \(P^3_4=\frac{4!}{(4-3)!}=24\): ABC, ACB, BAC, BCA, CAB, CBA, ...

The # of ways to visit 4 cities when order matters = \(P^4_4=\frac{4!}{(4-4)!}=24\): ABCD, ABDC, ADCD, ...

12 + 24 + 24 = 60.

Answer: C.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 2, 3, 5, 7 and 10. Thank you.



Why not 4C2x4C3x4C4?



Travel itinerary means you can start your travel from any city-say you start from B and then moved to A and other way round you can start from A and move to B-so you have two different itineraries.Itineraries literally means planned routes and so you have two different routes as I explained.
Intern
Intern
avatar
B
Joined: 15 Dec 2016
Posts: 2
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 400 Q43 V6
GPA: 2.5
Reviews Badge
A man wants to visit at least two of the four cities A, B, C  [#permalink]

Show Tags

New post 10 Jan 2017, 05:17
In this question ALL THE CITIES ARE CONNECTED TO ONE ANOTHER, .How you consider this piece of information.I am not getting this part. I am supposed to select at least two cities. could you please just give me a brief idea. how to solve this type of questions.
Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1329
Location: Malaysia
GMAT ToolKit User
A man wants to visit at least two of the four cities A, B, C  [#permalink]

Show Tags

New post 10 Jan 2017, 05:37
JusTLucK04 wrote:
We can also say:

4C2*2! + 4C3*3! + 4C4*4!

I am quite confused with this P n C terminologies..on where to use...so I go intutively..i.e First select the elements and then shuffle them with factorial (If required)...Veritas has an excellent guide on combinatorics..which combined with Bunuels Q bank is enough for 700+ Q on this topic


Bunuel Why we need 4C2*2!+ 4C3*3! + 4C4*4! as highlighted?
_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/
Intern
Intern
avatar
B
Joined: 08 Oct 2017
Posts: 31
GMAT ToolKit User
Re: A man wants to visit at least two of the four cities A, B, C  [#permalink]

Show Tags

New post 10 Jul 2018, 09:06
hazelnut
Ways to choose cities x ways to travel
At least 2 cities —> 6 ways (2 cities chose out 4) x 2! (Ways to travel to cities) = 12
3 cities —> 4 x 3! =24
4 cities —> 1 x 4! = 24
Total = 60 (C)
_________________
****Give me Kudos to get my GMAT club test access****
GMAT Club Bot
Re: A man wants to visit at least two of the four cities A, B, C   [#permalink] 10 Jul 2018, 09:06
Display posts from previous: Sort by

A man wants to visit at least two of the four cities A, B, C

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne