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How many 5 letter combinations can be made from the letters

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How many 5 letter combinations can be made from the letters  [#permalink]

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New post 18 Jul 2014, 10:53
2
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A
B
C
D
E

Difficulty:

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Question Stats:

71% (01:48) correct 29% (02:11) wrong based on 222 sessions

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How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once?

A. 21
B. 42
C. 120
D. 600
E. 720
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Posts: 61396
Re: How many 5 letter combinations can be made from the letters  [#permalink]

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New post 18 Jul 2014, 10:58
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6
goodyear2013 wrote:
How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once?

A. 21
B. 42
C. 120
D. 600
E. 720


{vowel}{X}{X}{X}{consonant}

VERMONT consists of 2 vowels and 5 consonants:

The number of way to choose a vowel for the first letter = \(C^1_2=2\).
The number of way to choose a consonant for the last letter= \(C^1_5=5\).

The number of ways to choose middle three letters out of 5 remaining letters = \(C^3_5=10\).
The number of arrangements of these three letters = 3! = 6.

Total = 2*5*10*6 = 600.

Answer: D.
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Re: How many 5 letter combinations can be made from the letters  [#permalink]

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New post 25 Feb 2016, 01:04
2
1
1
Vowel: E O

Consonants: V R M N T

First letter can be filled in 2 Ways ( As the question states that "first letter has to be a vowel")
Fifth letter can be filled in 5 Ways ( As the question states that "the last letter has to be a consonant")

Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and Fifth letter

Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
Fourth letter can be filled in 3 Ways

So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 3 ways x 5 ways = 600

Answer D
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Re: How many 5 letter combinations can be made from the letters  [#permalink]

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New post 25 Feb 2016, 03:06
i normally tend to do it using fill in the blanks

- - - - - the first place has condition which can be either O or E and the last place by V.R.M,N,T as for the 2nd 3rd and 4th we have the remaning ones

so its like first place =2
Last place 5
second place 5
third place 4 and 4th place 3

so number of combinations = 2*5*4*3*5 = 600

so 600 ways
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Re: How many 5 letter combinations can be made from the letters  [#permalink]

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New post 04 Aug 2017, 04:20
VERMONT has 2 vowels and 5 consonants.
Hence first letter can be chosen in 2 ways.
Hence last letter can be chosen in 5 ways.
Remaining 3 can be selected in 5*4*3 ways.
So total ways the letters can be arranged in that sequence
2*5*4*3*5=600 ways.
Option D.
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Re: How many 5 letter combinations can be made from the letters  [#permalink]

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New post 09 Jan 2020, 22:21
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Re: How many 5 letter combinations can be made from the letters   [#permalink] 09 Jan 2020, 22:21
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