Several children were playing in the ugly tree when suddenly they all fell.

Roger hit branches A, B, and C in that order on the way down.

Sue hit branches D, E, and F in that order on the way down.

Gillian hit branches G, A, and C in that order on the way down.

Marcellus hit branches B, D, and H in that order on the way down.

Juan-Phillipe hit branches I, C, and E in that order on the way down.

Mikey hit every branch A through I on the way down. Given only this information, in

how many different orders could he have hit these 9 branches on the way down?