SOLUTION: A meeting takes place between a diplomat and fifteen government officials. However, ten of the officials are actually spies. If the diplomat gives secret information to eight of th

Among 15 government officials there are 10 spies and 5 loyal officials, according to the condition.


So, to answer the problem's question, you actually should answer two questions:


        1.  In how many ways the groups of the 8 attendees can be formed of 15 officials ?

    and

        2.  In how many ways the groups of the 8 attendees can be formed of 15 officials under the condition 
            that each such group contains exactly 5 spies and 3 loyal diplomats ?


The answer to question #1 is:  in  =  = 6435 ways.

    It is the cardinality of the full space of events.


The answer to question #2 is:  in  . = * = 252*10 = 2520 ways.


And now the final answer is:  The probability under the problem's question is  = 0.3916   (rounded).