First of all, there are 25 ways a chairperson can be selected from a committee of 25 senators. When the chairperson is selected, only 24 people left. So there are 24 ways a vice chairperson can be selected after the chairperson is dicided.

So in total, there are 25x24=600 ways that a chairperson and a vice chairperson can be selected from a committee of 25 senators