Since 1 January 2013, every household has had to pay the so-called “Rundfunkbeitrag” (TV and radio licence fee). That means: It doesn’t matter how many people you share your flat with, as long as one person pays the fee the entire household is covered.
BAföG (German Federal Training Assistance Act) recipients may apply for an exemption from paying the Rundfunkbeitrag. If you or one of your flatmates are granted an exemption, the others won’t have to pay the fee either.
It’s best to apply for an exemption from paying licence fees within two months of having your BAföG application approved. You must do this in order for your Rundfunkbeitrag exemption to take effect retrospectively on the day your BAföG starts. If you don’t apply within two months, you will not be exempted until the following month.