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
• B. 1800
• C. 2160
• D. none of these

Answer 1

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 $2!$
$\therefore$ the number of ways are $\frac{5!5!}{2!2!2!}$=1800
Hence option B is correct