How many words can be formed from the letters of the word 'COURTEST' 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 'COURTEST' 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 'COURTEST'
The word 'COURTEST' consists of the following letters: C, O, U, R, T, E, S, T.

### 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. However, since Y is not present in the word 'COURTEST', it seems there is a misunderstanding in the question. Assuming the question meant to ask for the arrangement of the letters with C at the start and T at the end (since T appears twice), we will proceed with that assumption.

### Step 3: Determine the letters to arrange
With C fixed at the beginning and T fixed at the end, we are left with the letters O, U, R, E, S (5 letters) to arrange in the middle.

### Step 4: Calculate the number of arrangements
The number of ways to arrange these 5 letters is given by the factorial of the number of letters. Since all letters are distinct, we can use the formula for permutations:

\[ \text{Number of arrangements} = 5! \]

Calculating \(5!\):

\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]

### Conclusion
Thus, the total number of words that can be formed from the letters of the word 'COURTEST' with C as the first letter and T as the last letter is **120**.

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