Step 1 :Calculate the total number of arrangements with no restrictions: \(7! = 5040\)
Step 2 :Calculate the number of arrangements for consonants: \(4! = 24\)
Step 3 :Calculate the number of arrangements for vowels: \(3! = 6\)
Step 4 :Calculate the number of alternating arrangements: \(2 \times 24 \times 6 = 288\)
Step 5 :Calculate the number of arrangements with vowels in the middle: \(24 \times 6 = 144\)
Step 6 :\(\boxed{\text{Final Answer:}}\)
Step 7 :a) \(\boxed{5040}\) ways with no restrictions
Step 8 :b) \(\boxed{288}\) ways with consonants and vowels alternating
Step 9 :c) \(\boxed{144}\) ways with all vowels in the middle