14 government officials, 4 of them spies. A diplomat gives information to 10 at random, what is the probability that no secret information was given to spies?

Question

A meeting takes place between a diplomat and fourteen government officials. However four of the officials are actually spies. If the diplomat gives secret information to ten of the attendees at random, what is the probability that no secret information was given to the spies?

Answer 1

The number of ways to choose 10 people out of 14 people is given by ₁₄C₁₀ which is read "14 choose 10"  

 

(If you don't know what this symbol means or how to calculate its value then comment back)  

 

Only 1 of these combinations will result in no information being given to any of the 4 spies.  

 

Can you figure out the probability from these 2 facts?