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

It is currently 18 Jun 2019, 08:06

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

What is the probability that out of the combinations that can be made

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

Hide Tags

 
Intern
Intern
avatar
Joined: 20 Dec 2015
Posts: 2
What is the probability that out of the combinations that can be made  [#permalink]

Show Tags

New post 04 Feb 2016, 06:46
1
6
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

54% (02:58) correct 46% (02:49) wrong based on 67 sessions

HideShow timer Statistics

What is the probability that out of the combinations that can be made using all the letters of the word EXCESS, Jerome will randomly pick a combination in which the first letter is a vowel and the last letter is a consonant?

A 96/320
B 24/180
C 33/100
D 48/180
E 96/180
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7757
Re: What is the probability that out of the combinations that can be made  [#permalink]

Show Tags

New post 04 Feb 2016, 07:10
3
1
wufabif wrote:
What is the probability that out of the combinations that can be made using all the letters of the word EXCESS, Jerome will randomly pick a combination in which the first letter is a vowel and the last letter is a consonant?

A 96/320
B 24/180
C 33/100
D 48/180
E 96/180



Hi,
EXCESS has two Es and 2 Ss..
so different possible combinations= 6!/2!2!= 180..

lets see the possiblilties with the given restrictions..
lets put the starting letter as vowel E..
then remaining 5 places can be filled in 5!/2!= 60..
but this consists of second E as the last letter and we will have to subtract these ways from 60..

so when first and last places are occupied by E, the remaining 4 places can be filled by 4!/2!=12 ways..
so ways with the restrictions= 60-12= 48..

so prob= 48/180
D
hope it helps..
_________________
Intern
Intern
avatar
Joined: 20 Dec 2015
Posts: 2
Re: What is the probability that out of the combinations that can be made  [#permalink]

Show Tags

New post 04 Feb 2016, 07:39
Hey chetan2u!

Thank you for your fast response to my question.
Combinations are (hopefully not any longer) a great weakness of mine, so i do not yet understand how you derived the equations used for the possibilities.
Is there any link to a guide or forum post which i can use to refresh my combinations formulas from highschool in order to be able to reproduce your calculations?

Best regards
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7757
Re: What is the probability that out of the combinations that can be made  [#permalink]

Show Tags

New post 04 Feb 2016, 07:49
1
wufabif wrote:
Hey chetan2u!

Thank you for your fast response to my question.
Combinations are (hopefully not any longer) a great weakness of mine, so i do not yet understand how you derived the equations used for the possibilities.
Is there any link to a guide or forum post which i can use to refresh my combinations formulas from highschool in order to be able to reproduce your calculations?

Best regards


Hi,
i'll just explain how this equation has come..
EXCESS has 6 places...
the first place can be filled by any of the 6, next by remaining 5, and so on till you are left with only one place and one letter..
so ways=6*5*4..*1=6!..
but these 6! has duplication of Es and Ss..
example if you are taking 6 position as first E and 4 position for second E...
this will be same when you are taking 4 position as first E and 6th position for second E...
that is why we divide the answer by 2!, as these 2 places within two Es can be done in 2! ways..

so ways become 6!/2!2!..

Do practice these somes by putting combinations in the search tag..
and you will find theory too ..
_________________
Intern
Intern
avatar
Joined: 03 Aug 2015
Posts: 8
Re: What is the probability that out of the combinations that can be made  [#permalink]

Show Tags

New post 06 Feb 2016, 08:47
3
The total words can be formed with the letters EXCESS are: 6!/(2!*2!) = 180 (as we have two double letters, E and SS)

For the words given the restrictions we have 2 scenarios:

- The vowel is E and the consonant is S: 1*4!*1 = 4! = 24 (as we have only one option to the vowel, E, and one to the consonant, S)
- The vowel is E and the consonant is NOT S: 1*(4!/2!)*2 = 4! = 24 (as we have only one option to the vowel, E, and 2 options to the consonant, X or C, also we have a double letter, S, in the 4 words between the first and last letters)

Finally, the probability is (24+24)/180 = 48/180
Answer: D
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11386
Re: What is the probability that out of the combinations that can be made  [#permalink]

Show Tags

New post 30 Dec 2018, 21:19
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 Club Bot
Re: What is the probability that out of the combinations that can be made   [#permalink] 30 Dec 2018, 21:19
Display posts from previous: Sort by

What is the probability that out of the combinations that can be made

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


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