I'm wrapping up a bathroom remodel. An electrician came a while back and ran new wiring. He installed a plastic 4-gang box which will have a GFCI receptacle and 3 switches for a light above the vanity, an overhead light, and an overhead fan. The wiring is already in place; I just need to install the actual GFCI and switches. There are three cables coming into the top of the box: two with a black, a white, and a bare, and one with a black, a white, a red, and a bare. When he installed the wiring and box, he roughly pushed each group of wires into place. I made the attached diagram based on where it looked like the wires were supposed to end up. Does this look correct? Also, will the three switches be single pole switches? Thanks.
While the advice in other answers appears correct, it is critical to connect the "line" and "load" wires correctly to the GFCI. Here's a picture from a help page You can ignore the GFCI on the left.
You need to ground your switches -- Code requires it. And yes, standard single pole switches work here.
Also -- depending on where the fixtures are located, you may wish to put one or more of them on the load side of the GFCI. Make sure that the existing black and white wires on your diagram go to the LINE terminals on the GFCI outlet!
That looks correct. Your ground(bare) and neutral(white) will all be nutted together. Then the black and red wires (hot) will attach to the switches (all appear to be single pole since none are in a series)
The only thing I would suggest is making sure you ground the switches. Sometimes code will demand it, but it's also a good idea since it's a wet location.