To calculate the probability that two given persons are adjacent when six people seat themselves at a round table, we need to consider the total number of seating arrangements and the number of arrangements where the two given persons are adjacent.
Total Number of Seating Arrangements:
The total number of seating arrangements for six people at a round table can be calculated as (6-1)! = 5!, since we fix one person's position and arrange the remaining five people around the table.
Number of Arrangements with Two Given Persons Adjacent:
To calculate the number of arrangements where the two given persons are adjacent, we can consider them as a single entity. So we have 5 entities (including the pair of adjacent persons) to arrange around the table. The number of arrangements for these entities is (5-1)! = 4!.
Therefore, the probability that the two given persons are adjacent is given by:
Probability = Number of Arrangements with Two Given Persons Adjacent / Total Number of Seating Arrangements
= (4!) / (5!)
= 1/5
= 0.2 or 20%
So, the probability that the two given persons are adjacent when six people seat themselves at a round table is 0.2 or 20%.
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