Three computer tasks A, B, C each with 5 ordered parts: A1 through A5, B1 through B5, and C1 through C5, are being multi-tasked by my PC. Each task must execute its parts in order one through five. Thus A1 B1 B2 C1 C2 C3 C4 B3 A2 etc. is an acceptable order. Assume, that the choice of which task to work on next is chosen randomly, and that the next part of that task is then executed. What is the probability that after all 15 parts are complete, five parts of at least one task were executed consecutively? (Use Inclusion/Exclusion)
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