Probability of Combinations which have different probabilties.

I cannot figure this out. The problem goes A boy has a bag filled with balls:

1 red

2 green

4 Blue

7 White

A child plays a game in which he withdraws one ball, writes down its color, and then replaces the ball. In order to win the game he must write down at least one of each color of ball. What is the probability that this will happen on, or before the N-th trial???

I cannot figure this out. The problem goes A boy has a bag filled with balls:

1 red

2 green

4 Blue

7 White

A child plays a game in which he withdraws one ball, writes down its color, and then replaces the ball. In order to win the game he must write down at least one of each color of ball. What is the probability that this will happen on, or before the N-th trial???