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What percent of 5 letter combinations that can be made from

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Senior Manager
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What percent of 5 letter combinations that can be made from  [#permalink]

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New post 03 Aug 2014, 09:01
3
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A
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Difficulty:

  65% (hard)

Question Stats:

65% (02:12) correct 35% (02:38) wrong based on 159 sessions

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What percent of 5 letter combinations that can be made from the letters of the word VERMONT and in which each letter can be used only once are the combinations in which the first letter is a vowel and the last letter is a consonant?

A. 20%
B. 23.8%
C. 25%
D. 30.2%
E. 35%

In the order of the 5 digits
Desired: 2×(5×4×3)×5
All: 7×6×5×4×3
--> Desired / All = 5 / 21
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Re: What percent of 5 letter combinations that can be made from  [#permalink]

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New post 03 Aug 2014, 12:29
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1
a) noof combinations when all 5 letters are different = 7*6*5*4*3
b) noof combinations when first letter is vowel and last is consonant = 2c1*5c1*5*4*3

b/a = 5/21= 0.238

Hope it helps
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Re: What percent of 5 letter combinations that can be made from  [#permalink]

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New post 03 Aug 2014, 14:22
1
goodyear2013 wrote:
What percent of 5 letter combinations that can be made from the letters of the word VERMONT and in which each letter can be used only once are the combinations in which the first letter is a vowel and the last letter is a consonant?

A. 20%
B. 23.8%
C. 25%
D. 30.2%
E. 35%

In the order of the 5 digits
Desired: 2×(5×4×3)×5
All: 7×6×5×4×3
--> Desired / All = 5 / 21


TOTAL number of 5 letter combinations = 7P5 = 7!/2! = 3*4*5*6*7
There are 2 vowels: e,o and 5 consonants: v,r,m,n,t
If ABCDE is the required combination, A has 2 options, E has 5 options, B has 5, C has 4, and D has 3
Number of required combinations = 2*5*5*4*3

Answer = 2*5*5*4*3 / 3*4*5*6*7 = 5/21 = 23.8%

B!!!!!!!!!!! :-D
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Re: What percent of 5 letter combinations that can be made from  [#permalink]

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New post 12 Aug 2014, 08:45
goodyear2013 wrote:
What percent of 5 letter combinations that can be made from the letters of the word VERMONT and in which each letter can be used only once are the combinations in which the first letter is a vowel and the last letter is a consonant?

A. 20%
B. 23.8%
C. 25%
D. 30.2%
E. 35%

In the order of the 5 digits
Desired: 2×(5×4×3)×5
All: 7×6×5×4×3
--> Desired / All = 5 / 21


Similar question to practice: how-many-5-letter-combinations-can-be-made-from-the-letters-174612.html
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Re: What percent of 5 letter combinations that can be made from  [#permalink]

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New post 25 Feb 2016, 02:03
I like to solve these type of questions this way

VERMONT = 7 letters. , 5 consonants, 2 vowels

To fill : 5 Spaces

_ _ _ _ _

So, total number of combinations =

7 X 6 X 5 X 4 X 3

= 2520

Placing the restrictions : 1st letter must be vowel = 2 combinations. 5th letter must be consonant = 5 combinations

2 X 5 X 4 X 3 X 5 = 600


%age = 600/2520 = 23.8
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Re: What percent of 5 letter combinations that can be made from  [#permalink]

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New post 23 Dec 2018, 09:03
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Re: What percent of 5 letter combinations that can be made from &nbs [#permalink] 23 Dec 2018, 09:03
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