It depends a lot more on the power of the transmitter, not the
frequency...
In addition, it also depends on the filtering and authentication
algorithm of the remote control car, which if imperfect, may make
take in stray signals and go haywire. It will be good to use 16-bit
authentication along with some form of simplified CRC algorithms.
It may also be good to use a bandpass filter to get a cleaner
signal.
You should post this in homework forum for more help