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Probability that c7 sits in c8

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Two adults a1 and b1, and eight children c1, c2, ... , c8 board a bus
with 10 seats s1, s2, ... , s10. The adults board first and randomly
select seats. The children select seats in order with c1 selecting
first, c2 selecting second, and so on. Each child sits in the lowest
numbered seat available to them. What is the probability that c7 sits in
s8?

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Solution Summary

This solution is comprised of a detailed explanation to answer what is the probability that c7 sits in s8.

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Since the children have no option of which seat to take, this really
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