Each of the 108 students attending a conservatory of music plays at least one of the piano, harp, and clarinet. 67 play the piano, 46 play the harp, 32 play the clarinet, 19 play the piano and the harp, 13 play the harp and the clarinet, and 8 play the piano and the clarinet. How many play all three instruments? Hint: Let x represent the number of students who play all three instruments.
