A train will consist of 4 passenger cars, 2 cattle cars, and 3 luggage cars,

which are to be put in order at random.

A/ Mr. and Mrs. Atwood and their three daughters and two sons are boarding one of the passenger cars on the next stop.

i. In how many different orders can the members of the Atwood family enter the car?

ii. In how many of these orders does Mrs. Atwood precede Mr. Atwood?

iii. In how many of these orders does Mrs. Atwood and her two sons precede Mr. Atwood his three daughters?