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Question

The total number of words that can be made by writing the letters of the word PARAMETER so that no vowel is between two consonants is

A
1440
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B
1800
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C
2160
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D
none of these
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Solution

The correct option is B 1800
Given,
PARAMETER
no vowel is between two consonants i.e. all the consonants are together
let all the consonants be treated as one letter
hence now there are 5 letters which can be arranged in 5! ways as A and E are repeated so we divide it by 2!2!
Now 5 consonants can be arranged in 5! ways as R is repeating twice we should divide it by 2!
the number of ways are 5!5!2!2!2!=1800
Hence option B is correct
172312_133851_ans_d013f28b551d405f84efa44b8f925f61.png

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