A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is

Correct Option: 43 (Option 4)

Let F, T, and C denote the sets of members who can play football, tennis, and cricket respectively.

We are given the following values:
Total members, n(F ∪ T ∪ C) = 256
n(F) = 144
n(T) = 123
n(C) = 132
n(F ∩ T) = 58
n(C ∩ T) = 25
n(F ∩ C) = 63

Using the principle of inclusion-exclusion for three sets:
n(F ∪ T ∪ C) = n(F) + n(T) + n(C) - n(F ∩ T) - n(T ∩ C) - n(F ∩ C) + n(F ∩ T ∩ C)

Substituting the given values:
256 = 144 + 123 + 132 - 58 - 25 - 63 + n(F ∩ T ∩ C)
256 = 399 - 146 + n(F ∩ T ∩ C)
256 = 253 + n(F ∩ T ∩ C)
n(F ∩ T ∩ C) = 256 - 253 = 3

Now, we want to find the number of members who play only tennis. From a Venn diagram, the number of members who play only tennis is given by:
n(only T) = n(T) - n(F ∩ T) - n(C ∩ T) + n(F ∩ T ∩ C)
n(only T) = 123 - 58 - 25 + 3
n(only T) = 123 - 83 + 3 = 43

Thus, the number of members who can play only tennis is 43.