Runners on first and second base.
Ground ball to the third baseman. The third baseman fields the ball and steps on third base for the force out. He then attempts to throw the batter out at first base. The throw bounces before reaching the first baseman and rolls a long way into foul territory. The runner originally on first advances to second on the touch of the base and the throw, he goes to third base and scores on the E5 throw.
Batter advances to first base on the fielder’s choice (can’t assume the double play); he goes to second and third base on the E5 throw.
The ball is retrieved by the first baseman and thrown towards home plate. It comes in about 15 feet up the third base line, the catcher attempts to catch the throw, but it gets passed him and hits the dugout railing. The batter runs for home. The catcher picks up the ball and throws it to the pitcher who is covering home, the throw is over the pitcher’s head and the run scores.
The runner would have been safe even if the throw from the catcher to the pitcher been accurate, so that detail can be ignored. The errant throw by the first baseman cannot however, it is on the E3 throw that the batter advances home for the “little league home run.”