Question

How many four lettered words can be formed without repetition from the word $\text{FAILURE}$ such that all the words start with the vowels?

• A. $24$
• B. $840$
• C. $480$
• D. $60$

Answer 1

The correct option is C $480$

Given word is $\text{FAILURE}$ has $7$ letters out of which $4$ are vowels i.e. $\text{A, E, I, U}.$

We have to find number of $4$ lettered words starting from vowel which is equal to filling of $4$ vacant places with different number of possibilities.


So, first place have $4$ possibilities because only vowels can be filled in that place.

Now, no furthur constraint is present for rest of the three vacant places.

So, $2^{nd},3^{rd}$ and $4^{th}$ place can be filled in $6,5$ and $4$ number of ways.

Total number of $4$ lettered words formed will be $4\times 6\times 5\times 4=480$