Question

The number of permutations that can be made out of the letters of the word "EQUATION" which start with a consonant and end with a consonant is:

• A. $2!\times 6!$
• B. $3!\times 6!$
• C. $3!\times 5!$
• D. $2!\times 5!$

Answer 1

Answer: (B)

$3!\times 6!$

The word 'EQUATION' has 5 vowels "E,U,A,I,O" and 3 consonants "T,Q and N".
The consonant for the first place can be selected in 3 ways.
Then, the consonant for the last place can be selected in 2 ways.
The other 6 places in between can be occupied by the remaining 6 letters in 6 ! ways.
Hence, the total number of ways $=3\times 2\times 6!$
Hence, option B is correct.