How many players are there who are girls but not a coach?

Step 1: Identify the relevant regions in the Venn Diagram

• The question asks for the number of individuals who are players and girls but explicitly not a coach.
• In the Venn diagram:
- The green circle represents "players".
- The purple circle represents "girls".
- The blue circle represents "coach".

Step 2: Find the intersection of "players" and "girls"

• The intersection of the "players" circle (green) and the "girls" circle (purple) includes the numbers 16 and 30.
• These represent individuals who are both players and girls.

Step 3: Exclude individuals who are also "coaches"

• The number 30 is in the intersection of all three circles (players, girls, and coach).
• This means these 30 individuals are players, girls, AND coaches.
• Since the question asks for not a coach, we exclude 30.

Step 4: Determine the final count

• The number in the intersection of "players" and "girls" but outside the "coach" circle is 16.

Answer:

The number of players who are girls but not a coach is 16.