I just want to know if my thinking in doing this problem is correct:
If 2 of the 4 expressions x+y, x+5y, x-y, 5x-y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2 where b is any integer?
4 properties, 2 choices = 4!/2! ways of choosing since order doesn't matter. so 12.
to get the expression x^2-(by)^2 we can only have choices (x+y and x-y) , (x+5y and x-y)
so 2/12 = 1/6 chance.
If 2 of the 4 expressions x+y, x+5y, x-y, 5x-y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2 where b is any integer?
4 properties, 2 choices = 4!/2! ways of choosing since order doesn't matter. so 12.
to get the expression x^2-(by)^2 we can only have choices (x+y and x-y) , (x+5y and x-y)
so 2/12 = 1/6 chance.
