Question

How many words with the letters of the word “CARAVELLE” can be formed which starts with R?
A. 8!
B. 5040
C. 1080
D. None of these

Answer 1

Hint: Here the given word has 9 letters. We have to start the required word with R. Remaining letters will be used to form the word. So there can be directly 8! Words. This is simple to solve because there is no such condition on the word formation.

Complete step by step solution:
Given word is “CARAVELLE”
Now R is used in the initial place. So there are 8 letters left.
But A, L and E are repeated. But there is no bound or condition for the repetition of the letter.
 So the total words so formed will be 8!.
This is the correct answer. So option A is correct.
So, the correct answer is “Option A”.

Note: Note that the letters A, E and L are repeated.If the letter repetition is not allowed then, we will write the number of words so formed will be,
\[ = \dfrac{{8!}}{{2! \times 2! \times 2!}}\]
Writing the values of the factorial,
\[ = \dfrac{{40320}}{8}\]
On dividing by 8 we get,
\[ = 5040\]
This will be the answer then.