6 balls marked as 1,2,3,4,5 and 6 are kept in a box. Two players A and B start to take out 1 ball at a time from the box one after another without replacing the ball till the game is over. The number marked on the ball is added each time to the previous sum to get the sum of numbers marked on the balls taken out. If this sum is even, then 1 point is given to the players. the first player to get 2 points is declared winner. at the start of the game, the sum is 0. if A starts to take out the ball, find the number of ways in which the game can be won.

Answer

96

Explanation

Denoting `A_(1),B_(1),A_(2) and B_2` for their taking out the ball, a chart is made to denote the winner.

`therefore`Total number of ways in which the game can be won when A starts the game =36+36+18+6=96.