find the probability that 3 people are born on different months from each other
The Attempt at a Solution
So here's my reasoning. There are 3 people X1, X2, X3. Let (Xi,Xj) denote the pair have different birthmonths. P[(X1,X2) and (X2,X3) and (X3,X1)]=P(X1,X2)*P(X2,X3)*P(X3,X1)
thus P[(X1,X2) and (X2,X3) and (X3,X1)]=P(X1,X2)*P(X2,X3)*P(X3,X1)=(11/12)^3
But that is not the answer. My book said the answer is (11/12)*(10/12).
I dont see what is wrong with my reasoning. for the 3 to have different birthmonths, any two would have different birthmonths. X1 different from X2, X2 from X3, X3 from X1.