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yes this is a college project but our professor did not teach us well in this section....
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Are you sure he doesn't want you to figure something out yourself? In all honesty, this looks like a very simple design task that should be do-able in a few hours...
Here's how I would approach the project:
First, you need to set up some sort of debounced button, with a circuit to do edge detection. You want there to be a signal that's asserted for one clock cycle when the button goes down. That signal is used as an enable for your state machine (since it's not cool to abuse clock inputs). The state machine has outputs for the 3 lights and the transmitter.
There are two ways to do the transmitter / receiver: either have it transmit when something changes, or have it constantly transmit the present state. The absolute simplest-to-understand way to do either one would probably be to transmit tones through RF modules--the tx input could be a few 555's with a MUX, and the receiver can be one or more xx567 tone decoders. This gets around the limitations in most RF modules (they need a minimum number of transitions / second) without using complicated encoding schemes.