Problem #WSP-000052

Problem

Rithika is choosing songs for a party tonight. She has $214$ songs in her library and wants to use $50$ for the party. She wants to play each song only once. In how many ways can she compose her playlist?
Now suppose that each song has a different duration, and Rithika wants the songs to play in order from the longest chosen to the shortest chosen. How many ways can she choose her playlist now? (You can leave the answer as a formula).