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Question: A digital continuity consultant in California organizes a virtual archive session with 8 staff members and 5 community volunteers. If they sit around a circular video conference table with seats distinguishable only by position relative to others, how many distinct seating arrangements are possible?
Solution: For circular arrangements of $n$ distinguishable people, the number of distinct arrangements is $(n-1)!$. Here, there are $8 + 5 = 13$ individuals. Thus, the number of distinct seating arrangements is $(13-1)! = 12!$.
Question: A public engagement officer in London rolls a fair 10-sided die (faces numbered 1 to 10) four times to simulate species observation scores. What is the probability that exactly two rolls result in a prime number?