Question

The different words beginning and ending with a vowel that can be made with all the letters of the word $EQUATION$ is:

• A. $14400$
• B. $4320$
• C. $864$
• D. $1440$

Answer 1

The correct option is A $14400$

$EQUATION$ has $5$ vowels - $A,E,I,O,U$

For the word to begin with an vowel, there are $5$ possibilities. ie., either of the 5 vowels.

For the word to end with an vowel, there are $4$ possibilities. ie., either of the 4 vowels left out after one of the vowels's occupy the first place.

Now we are left with $6$ places in between the first and the last. The total no of possible arrangements for these 6 places is $6!$

Hence the total no. of words formed $=5\times 6!\times 4$

$=5\times (6\times 5\times 4\times 3\times 2\times 1)\times 4$

$=14400$