If 2 of the 4 expressions x+y,X=5y,x-y and 5x-y are chosen at random. what is the probabilty that their product will be of the form of x^2-(by)^2 , where b is an integer? ans 1/6
Only (x+y)(x-y) can give the result in the form of x^2-(by)^2 , which is x^2-1y^2.
Now, we have 4 different expressions, so let's see how many different pairs we can have: 4!/2!(4-2)! = 6. And because there is only one pair that satisfies us, therefore the probability of drawing it is 1/6.
