In Problem P15.8, it was decided to add five additional channels, (f₆, f₇, f₈, f₉, f₁₀) while keeping the frequency hopping sequence to five bands. Is it advisable to maintain frequency hopping within each of the channels (f₁, f₂, f₃, f₄, f₅) and (f₆, f₇, f₈, f₉, f₁₀), or it is better to select five channels among the bands (f₁, f₂, f₃, f₄, f₅  , f₆, f₇, f₈, f₉, f₁₀)? Explain your answer with some quantitative measures.

Data from in problem P15.8

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P15.8. In a hypothetical wireless system, five adjacent frequency bands (f, f, S3, S4. fs) are allowed for frequency hopping sequences. Enumerate how many different hopping sequences are possible and prove their correctness.