Question

A publishing firm evaluated $160$ manuscript submissions based on three quality criteria: Plot Originality ($P$), Character Development ($C$), and Dialogue Quality ($D$). Each manuscript was evaluated against all three criteria.

- $75$ manuscripts met the criteria for Plot Originality ($P$).
- $80$ manuscripts met the criteria for Character Development ($C$).
- $70$ manuscripts met the criteria for Dialogue Quality ($D$).
- $30$ manuscripts met the criteria for both Plot Originality and Character Development ($P \cap C$).
- $25$ manuscripts met the criteria for both Character Development and Dialogue Quality ($C \cap D$).
- $20$ manuscripts met the criteria for both Plot Originality and Dialogue Quality ($P \cap D$).
- $10$ manuscripts met all three criteria ($P \cap C \cap D$).

How many manuscripts met exactly one of the three criteria?