Final answer:
The number of different 4-letter permutations that can be formed from the letters in the word decagon is 840.
Step-by-step explanation:
The number of different 4-letter permutations that can be formed from the letters in the word decagon can be calculated using the concept of permutations. In this case, there are 7 letters in the word decagon. Therefore, the number of different 4-letter permutations is represented by the notation 7P4.
Using the formula for permutations, we have:
7P4 = 7! / (7 - 4)! = 7! / 3! = 7 × 6 × 5 × 4 = 840
Hence, there are 840 different 4-letter permutations that can be formed from the letters in the word decagon.