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

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Senior Manager
Joined: 21 Oct 2013
Posts: 408
How many 5 letter combinations can be made from the letters  [#permalink]

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18 Jul 2014, 10:53
2
8
00:00

Difficulty:

35% (medium)

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
Math Expert
Joined: 02 Sep 2009
Posts: 61396
Re: How many 5 letter combinations can be made from the letters  [#permalink]

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18 Jul 2014, 10:58
3
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.

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##### General Discussion
Intern
Joined: 25 Jun 2014
Posts: 42
GMAT 1: 690 Q48 V37
WE: Operations (Computer Software)
Re: How many 5 letter combinations can be made from the letters  [#permalink]

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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

Intern
Joined: 24 Feb 2016
Posts: 2
Re: How many 5 letter combinations can be made from the letters  [#permalink]

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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
Manager
Joined: 18 Jun 2017
Posts: 58
Re: How many 5 letter combinations can be made from the letters  [#permalink]

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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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Joined: 09 Sep 2013
Posts: 14124
Re: How many 5 letter combinations can be made from the letters  [#permalink]

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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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