How many words can be formed from the letters of the word 'COURTESY' whose first letter is C and the last letter is Y?

Options

A. 6!
B. 8!
C. 2(6)!
D. 2(7)!

Answer

To solve the problem of how many words can be formed from the letters of the word 'COURTESY' with the first letter as C and the last letter as Y, we can follow these steps:

### Step 1: Identify the letters in the word
The word 'COURTESY' consists of the following letters: C, O, U, R, T, E, S, Y. There are a total of 8 letters.

### Step 2: Fix the first and last letters
According to the problem, the first letter must be C and the last letter must be Y. Therefore, we can represent the arrangement as follows:

C _ _ _ _ _ _ Y

### Step 3: Count the remaining letters
After fixing C and Y, we have the following letters left to arrange: O, U, R, T, E, S. This gives us a total of 6 letters remaining.

### Step 4: Calculate the arrangements of the remaining letters
The number of ways to arrange these 6 letters is given by the factorial of the number of letters. Thus, we calculate:

Number of arrangements = 6! (6 factorial)

### Step 5: Compute the factorial
Now, we compute 6!:

6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

### Final Answer
Therefore, the total number of words that can be formed from the letters of the word 'COURTESY' with C as the first letter and Y as the last letter is **720**.

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