It is currently 13 Dec 2017, 07:17

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

There are 6 distinct letters of the English alphabet and 4 d

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

Hide Tags

Intern
Intern
avatar
Joined: 05 Feb 2014
Posts: 6

Kudos [?]: 15 [0], given: 4

There are 6 distinct letters of the English alphabet and 4 d [#permalink]

Show Tags

New post 06 Feb 2014, 02:15
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

57% (01:53) correct 43% (01:53) wrong based on 91 sessions

HideShow timer Statistics

There are 6 distinct letters of the English alphabet and 4 distinct digits. all possible 6 character apha-numero codes are generated using any 4 letters of the alphabet and any 2 available digits. If in any given code, the characters are all distinct, then what is the maximum number of such codes that can be generated?

A. 4320
B. 64800
C. 8800
D. 22000
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Feb 2014, 03:33, edited 1 time in total.
RENAMED THE TOPIC.

Kudos [?]: 15 [0], given: 4

Expert Post
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4550

Kudos [?]: 8950 [0], given: 111

Re: permutation and combination [#permalink]

Show Tags

New post 06 Feb 2014, 13:03
Expert's post
3
This post was
BOOKMARKED
ratnanideepak wrote:
there are 6 distinct letters of the English alphabet and 4 distinct digits. all possible 6 character apha-numero codes are generated using any 4 letters of the alphabet and any 2 available digits. If in any given code, the characters are all distinct, then what is the maximum number of such codes that can be generated?

A. 4320
B. 64800
C. 8800
D. 22000

Dear ratnanideepak
I'm happy to respond. :-) There seems to be a couple problems here. First of all, there are only four answer choices, whereas all GMAT Quant questions have five choices. On the real GMAT, and on all better prep sources, numerical answers always appear in numerical order, at least for positive integers.

From the six letters, we need four distinct letters
# of combinations = 6C4 = 15
From the four numerals, we need 2 distinct digits
4C2 = 6
Once we have our unique four letter and our unique 2 digits, we can put them in any order: each new order would be a different code. The number of orders would be
6! = 720

Now, we use the Fundamental Counting Principle. See:
http://magoosh.com/gmat/2012/gmat-quant-how-to-count/
Total number of codes equals = 15*6*720
Without a calculator, first do 15*6 = 90. Then, 90 = 100 - 10, so
720*90 = 720*(100 - 10) = 72000 - 7200 = 64800
Answer = (B)

Does all this make sense?
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Kudos [?]: 8950 [0], given: 111

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14874

Kudos [?]: 287 [0], given: 0

Premium Member
Re: There are 6 distinct letters of the English alphabet and 4 d [#permalink]

Show Tags

New post 13 Mar 2016, 05:51
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 287 [0], given: 0

Manager
Manager
avatar
Joined: 09 Jun 2015
Posts: 100

Kudos [?]: 9 [0], given: 0

Re: There are 6 distinct letters of the English alphabet and 4 d [#permalink]

Show Tags

New post 13 Mar 2016, 07:14
ratnanideepak wrote:
There are 6 distinct letters of the English alphabet and 4 distinct digits. all possible 6 character apha-numero codes are generated using any 4 letters of the alphabet and any 2 available digits. If in any given code, the characters are all distinct, then what is the maximum number of such codes that can be generated?

A. 4320
B. 64800
C. 8800
D. 22000


4 letter from 6 can be selected in 6C4 ways or 15 ways
2 numbers from 4 can be selected in 4C2 ways or 6 ways.
Now, we have selected 6 characters in 15*6 = 90 ways.
The 6 characters can be arranged in 6! ways or 720 ways.
Therefore, the total number of codes is 90*720 = 64800

Kudos [?]: 9 [0], given: 0

Manager
Manager
User avatar
B
Joined: 21 Jul 2017
Posts: 89

Kudos [?]: 9 [0], given: 67

Location: India
Concentration: Social Entrepreneurship, Leadership
GMAT 1: 650 Q47 V33
GPA: 4
CAT Tests
Re: There are 6 distinct letters of the English alphabet and 4 d [#permalink]

Show Tags

New post 29 Sep 2017, 22:22
Total number of digits in the code is 6.
Out of this 6, 4 are alphabets = 6C4 ways=15
The other 2 are numeric digits = 4C2 ways=6

Now these 6 digits can be arranged among themselves in 6! ways.
So, the answer is 15*6*6!=64800

Kudos [?]: 9 [0], given: 67

Re: There are 6 distinct letters of the English alphabet and 4 d   [#permalink] 29 Sep 2017, 22:22
Display posts from previous: Sort by

There are 6 distinct letters of the English alphabet and 4 d

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.