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# How many 7 letter words can be constructed using 26 letters

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Intern
Joined: 26 Mar 2006
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How many 7 letter words can be constructed using 26 letters [#permalink]

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12 Apr 2006, 20:09
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How many 7 letter words can be constructed using 26 letters of the alphabet if each word contains 3 vowels (repetitions allowed)

a) (21^4)*(5^3)
b) (21^4)*(5^3)*7!
c) {(21^4)*(5^3)*7!}/4!*3!
d) 21C4*5C3*7!
e) None of these

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VP
Joined: 29 Dec 2005
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Re: P&C - 7 letter word [#permalink]

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12 Apr 2006, 21:28
chillpill wrote:
How many 7 letter words can be constructed using 26 letters of the alphabet if each word contains 3 vowels (repetitions allowed)

a) (21^4)*(5^3)
b) (21^4)*(5^3)*7!
c) {(21^4)*(5^3)*7!}/4!*3!
d) 21C4*5C3*7!
e) None of these

total = 26
vowels (a, e, i, o, and u) = 5
consonants = 21

no of ways 3 vowels can be selected from 5 vowels = 5c3
no of ways 4 (7-3) consonants can be selected from 21 consonants= 21c4
no of ways 7 words can be arranged = 7!
so multiply all then its

(D) 21C4*5C3*7!

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Director
Joined: 10 Oct 2005
Posts: 713

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Location: Madrid
Re: P&C - 7 letter word [#permalink]

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12 Apr 2006, 21:39
Professor wrote:
chillpill wrote:
How many 7 letter words can be constructed using 26 letters of the alphabet if each word contains 3 vowels (repetitions allowed)

a) (21^4)*(5^3)
b) (21^4)*(5^3)*7!
c) {(21^4)*(5^3)*7!}/4!*3!
d) 21C4*5C3*7!
e) None of these

total = 26
vowels (a, e, i, o, and u) = 5
consonants = 21

no of ways 3 vowels can be selected from 5 vowels = 5c3
no of ways 4 (7-3) consonants can be selected from 21 consonants= 21c4
no of ways 7 words can be arranged = 7!
so multiply all then its

(D) 21C4*5C3*7!

10x you are really an El Professore)))
_________________

IE IMBA 2010

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Director
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13 Apr 2006, 00:29
Think that since repetitions are allowed it should be B)
Four consonants can be selected each in 21 ways, 3 vowels in 5 ways each and they can have 7! orderings. Now if the words have to be different then we come to A)

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Director
Joined: 24 Oct 2005
Posts: 658

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Location: London

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13 Apr 2006, 03:17
The 7 letter word can be

V V V C C C C which can be arranged in 7! ways.

Each V can be any of the 5 vowels.
Each C can be any of the 21 Consonants - since repetition is allowed.

(5*5*5 * 21*21*21*21 ) * 7!

Ans = B

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Manager
Joined: 09 Feb 2006
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Location: New York, NY

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13 Apr 2006, 07:01
I thought the words do have to be different. This would give us A, correct?

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VP
Joined: 28 Mar 2006
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13 Apr 2006, 15:25
BG is right...D is correct

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VP
Joined: 29 Dec 2005
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13 Apr 2006, 17:56
BG wrote:
Think that since repetitions are allowed it should be B)
Four consonants can be selected each in 21 ways, 3 vowels in 5 ways each and they can have 7! orderings. Now if the words have to be different then we come to A)

you are right. i didnot cinsider "repititon."

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Senior Manager
Joined: 24 Jan 2006
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14 Apr 2006, 08:17
YES! I care about repetition

(5*5*5 * 21*21*21*21) * 7!

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Senior Manager
Joined: 08 Sep 2004
Posts: 257

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Location: New York City, USA

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14 Apr 2006, 20:56
Professor wrote:
BG wrote:
Think that since repetitions are allowed it should be B)
Four consonants can be selected each in 21 ways, 3 vowels in 5 ways each and they can have 7! orderings. Now if the words have to be different then we come to A)

you are right. i didnot cinsider "repititon."

But even if you consider repetition, A should not be the answer. I think C is the correct Answer.

- Vipin

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14 Apr 2006, 20:56
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# How many 7 letter words can be constructed using 26 letters

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