How many melodies? #2

Probability Level 2

My toy piano keyboard has 7 distinct white notes: letters A-G in English alphabet. I'm going to create a melody by playing three random notes. I am not allowed to repeat any notes and the melody cannot be ended with E, F or G. How many different melodies can I play?

Examples:

C G A is permitted.
A F A isn't permitted because of repetition.
A B E is not permitted because of last note rule.