1. **State the problem:** We want to find the number of ways to order the letters of the word KITCHEN such that the first letter is a consonant and the last letter is a vowel. 2. **Identify the letters:** The word KITCHEN has 7 letters: K, I, T, C, H, E, N. 3. **Identify consonants and vowels:** - Consonants: K, T, C, H, N (5 consonants) - Vowels: I, E (2 vowels) 4. **Choose the first and last letters:** - First letter (must be consonant): 5 choices - Last letter (must be vowel): 2 choices 5. **Arrange the remaining letters:** After choosing the first and last letters, 5 letters remain to be arranged in the middle positions. Number of ways to arrange these 5 letters is $$5! = 120$$. 6. **Calculate total number of arrangements:** Total ways = (choices for first letter) \times (choices for last letter) \times (arrangements of middle letters) $$5 \times 2 \times 120 = 1200$$ **Final answer:** There are 1200 ways to order the letters of KITCHEN starting with a consonant and ending with a vowel.