Each of three different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned? Options
A) 1/8
B) 1/6
C) 1/9
D) 3/8
E) 1/2
I was just going over probability questions.   can some one explain me what's wrong in my approach here.   Probability of choosing one right key out of 3 is 1/3.   Probablity of choosing another right key is 1/3.   since the question is asking for 2 right keys , probability is multiplication of both = 1/3 * 1/3 = 1/9.   Ans 1/9
<result>C</result>
Each of three different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?