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

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

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04 Feb 2016, 06:46
1
6
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Difficulty:

65% (hard)

Question Stats:

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

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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
Joined: 02 Aug 2009
Posts: 7757
Re: What is the probability that out of the combinations that can be made  [#permalink]

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04 Feb 2016, 07:10
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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..
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Joined: 20 Dec 2015
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Re: What is the probability that out of the combinations that can be made  [#permalink]

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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
Joined: 02 Aug 2009
Posts: 7757
Re: What is the probability that out of the combinations that can be made  [#permalink]

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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 ..
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Joined: 03 Aug 2015
Posts: 8
Re: What is the probability that out of the combinations that can be made  [#permalink]

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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
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Re: What is the probability that out of the combinations that can be made  [#permalink]

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30 Dec 2018, 21:19
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Re: What is the probability that out of the combinations that can be made   [#permalink] 30 Dec 2018, 21:19
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