How many words beginning with C and ending with Y can be formed by using the letters of the word 'COURTESY' ?

Answer

To solve the problem of how many words beginning with 'C' and ending with 'Y' can be formed using the letters of the word 'COURTESY', we can follow these steps:

### Step-by-Step Solution:

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

2. **Fix the First and Last Letters**: Since we want the words to start with 'C' and end with 'Y', we can fix 'C' at the beginning and 'Y' at the end. This gives us the structure: C _ _ _ _ _ _ Y.

3. **Count the Remaining Letters**: After fixing 'C' and 'Y', we have the remaining letters: O, U, R, T, E, S. This means we have 6 letters left to arrange in the middle.

4. **Calculate the Arrangements**: The number of ways to arrange these 6 letters is given by the factorial of the number of letters, which is 6!.

\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \]

5. **Conclusion**: Therefore, the total number of words that can be formed beginning with 'C' and ending with 'Y' using the letters of 'COURTESY' is 720.

### Final Answer:
The total number of words beginning with 'C' and ending with 'Y' that can be formed using the letters of the word 'COURTESY' is **720**.

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