Answer:
Explanation:
To find the number of ways the letters of the word AFFECTION can be arranged while keeping the vowels in their natural order and ensuring that the two F's do not come together, we can break down the problem into separate steps.
Step 1: Determine the arrangement of the vowels (AEIO). Since the vowels need to be in their natural order, we can consider them as one unit. So, the vowels can be arranged in 1 way.
Step 2: Determine the arrangement of the remaining consonants (FFCTN). Again, since the two F's cannot come together, we need to consider the F's as separate entities. The remaining consonants can be arranged in 5! (5 factorial) ways.
Step 3: Combine the arrangements from Steps 1 and 2. The vowels can be arranged in 1 way, and the consonants can be arranged in 5! ways.
Therefore, the total number of arrangements is 1 × 5! = 1 × 120 = 120.
Hence, there are 120 ways to arrange the letters of the word AFFECTION while keeping the vowels in their natural order and ensuring that the two F's do not come together.