Ventilating a good sized closet grow

I'm currently setting up a closet grow (7' x 3') with one 400w MH/HPS to grow 4 or 5 Easy Ryders in soil (LR2xAK-47).

The closet is in an unused bedroom that is climate controlled via the home's central a/c. My initial thought was to leave the door open and the ceiling fan in the room running to circulate air in and out of the closet. However, I am worried about the smell outside of this room.

1. I don't have a huge budget for ventilation. Is it possible that I could close off the door and run two home depot duct fans to keep the closet cool. Coupled with a standing fan blowing air up and away from the plants inside the closet.

2. If I do leave the door open, what would be the best way to decrease the smell that would be leaving the room. Is it possible that I could create an odor-eliminator of sorts that could blow out of the room.

I'm not too worried if this room smells, I just do not want the rest of the house to smell like weed as I've heard this strain can be quite pungent while flowering.

Should add the closet is also about 7' tall

My plan is to leave the closet door open as I don't have the resources at the moment for a decent exhaust fan.

I will be growing in a closet that is climate-controlled with the rest of the house at 76-78 degrees. I will have at least one oscilatting fan, blowing the heat up and away from the lights and plants.

I am assuming that with this setup and because I am leaving the closet open to the room I will not have problems with the temp going over the low 80's.

Does anyone have experience with a similar setup and how much of an issue I would have with odor? My thought is that I could setup a shoebox filled with carbon that I could blow a PC fan through. Just don't know how effective this will be against 4-5 plants in flower. Any other methods to controlling odor when a direct exhaust is not an option??

Thanks anyone for any help/experiences in advance.