Among 17 government officials there are 10 spies and 7 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 17 officials ?

    and

        2.  In how many ways the groups of the 8 attendees can be formed of 17 officials under the condition that each such group 
            contains exactly 5 spies and 3 loyal diplomats ?


The answer to question #1 is:  in  =  = 24310 ways.

    It is the cardinality of the full space of events.


The answer to question #2 is:  in  . = * = 252*35 = 8820 ways.


And now the final answer is:  The probability under the problem's question is  = 0.3628 (approximately).