100 m Sprint

Discrete Mathematics Level 4

The following 8 sprinters will participate in a fictitious 100 m sprint:
Usain Bolt: Jamaica,
Yohan Blake:Jamaica,
Asafa Powell :Jamaica,
Tyson Gray :USA,
Richard Thompson :Trinidad and Tobago,
Donovan Bailey: Canada,
Olusoji Fasuba: Nigeria, and
Frankie Fredericks: Namibia

If the TWO rules below need to be followed, how many different lane assignments are possible?

  1. NO two sprinters from the same country can be in adjacent lanes.
  2. The outside lanes ( 1 and 8) can't be occupied by sprinters from the same country.

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