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In how many ways can 4 consonants and 3 vowels be arranged in a row so

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Bunuel
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In how many ways can 4 consonants and 3 vowels be arranged in a row so [#permalink] New post   02 Mar 2021, 06:45
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In how many ways can 4 different consonants and 3 different vowels be arranged in a row so that the first and the last places are occupied by consonants ?

A. 360
B. 720
C. 900
D. 1080
E. 1440
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E
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CrackverbalGMAT
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Re: In how many ways can 4 consonants and 3 vowels be arranged in a row so [#permalink] New post   02 Mar 2021, 06:57
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There are 7 letters in total. Since we have a restriction, we satisfy the same first.

We can pick and arrange 2 consonants out of 4 in 4C2 * 2! = 4P2 = 12 ways

The remaining 5 letters can be arranged in 5! = 120 ways

The total arrangements = 12 * 120 = 1440


Option E

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Re: In how many ways can 4 consonants and 3 vowels be arranged in a row so [#permalink] New post   30 Dec 2023, 11:25
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CrackverbalGMAT wrote:
There are 7 letters in total. Since we have a restriction, we satisfy the same first.

We can pick and arrange 2 consonants out of 4 in 4C2 * 2! = 4P2 = 12 ways

The remaining 5 letters can be arranged in 5! = 120 ways

The total arrangements = 12 * 120 = 1440


Option E

Arun Kumar


What gave you the que you needed to deduce that all consonants aren't the same? I.e. why do we have to pick and arrange consonants if we do not know if they are the same or not? For all we know, all consonants could be the same letter.
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Re: In how many ways can 4 consonants and 3 vowels be arranged in a row so [#permalink] New post   30 Dec 2023, 14:04
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Khwarizmi wrote:
CrackverbalGMAT wrote:
There are 7 letters in total. Since we have a restriction, we satisfy the same first.

We can pick and arrange 2 consonants out of 4 in 4C2 * 2! = 4P2 = 12 ways

The remaining 5 letters can be arranged in 5! = 120 ways

The total arrangements = 12 * 120 = 1440


Option E

Arun Kumar


What gave you the que you needed to deduce that all consonants aren't the same? I.e. why do we have to pick and arrange consonants if we do not know if they are the same or not? For all we know, all consonants could be the same letter.


Yes, the question should have mentioned that all letters are distinct. Issue fixed, thanks for pointing it out!
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Khwarizmi
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Re: In how many ways can 4 consonants and 3 vowels be arranged in a row so [#permalink] New post   30 Dec 2023, 17:16
Bunuel wrote:
Khwarizmi wrote:
CrackverbalGMAT wrote:
There are 7 letters in total. Since we have a restriction, we satisfy the same first.

We can pick and arrange 2 consonants out of 4 in 4C2 * 2! = 4P2 = 12 ways

The remaining 5 letters can be arranged in 5! = 120 ways

The total arrangements = 12 * 120 = 1440


Option E

Arun Kumar


What gave you the que you needed to deduce that all consonants aren't the same? I.e. why do we have to pick and arrange consonants if we do not know if they are the same or not? For all we know, all consonants could be the same letter.


Yes, the question should have mentioned that all letters are distinct. Issue fixed, thanks for pointing it out!


Give me my first kudos bro :))
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Re: In how many ways can 4 consonants and 3 vowels be arranged in a row so [#permalink]
30 Dec 2023, 17:16
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