To find the number of members who can play only tennis, we apply the principle of inclusion-exclusion to calculate the number of members who can play any of the games. Let:
Applying the principle of inclusion-exclusion:
\( N(F \cup T \cup C) = F + T + C - FT - TC - FC + N(F \cap T \cap C) \)
where \(N(F \cap T \cap C)\) is the number of members who can play all three games. Every member plays at least one game, so \( N(F \cup T \cup C) = 256 \).
Substitute the known values:\( 256 = 144 + 123 + 132 - 58 - 25 - 63 + N(F \cap T \cap C) \)
\( 256 = 339 - 146 + N(F \cap T \cap C) \)
\( 256 = 193 + N(F \cap T \cap C) \)
\( N(F \cap T \cap C) = 256 - 193 = 63 \)
Now, calculate the number of members who can play only tennis:
Therefore, the number of members who can play only tennis is 43.