4. A set of 7?. fair dice is thrown. All those that land on six are put aside, and the others are again thrown. This is repeated until each die lands on six. Let N denote the number of rounds needed. (For instance, suppose n = 3 and that in the rst round exactly two of the dice land on six. Then the other die will be thrown, and if it lands on six on the second throw after the rst round, then N = 3.) Let m\" = E[N]. (a) Derive a recursion formula for m\" and use it to calculate mm, 11 = 2, 3, 4, 5. (b) Let M denote the total number of rolls of all the no dice in all the N rounds together. Find E[M]