79. Initially in the first box there are 1 black ball and 1 white ball and in the second boxthere is a white ball. Tom choose a ball randomly from the first box, put it into thesecond box, then choose a ball randomly from the second box and put it back to the firstbox. The above process is called a “round”. After the third round, the probability that thetwo balls in the first box are of the different colors is nm(in the reduced fraction) . Findthe value of m n + .
(A) 107
(B) 109
(C) 111
(D) 113