We can draw the Venn diagram,
Given that,
- $ n (\text{F} \cup \text{T} \cup \text{C}) = 256 $
- $ n (\text{F}) = 144 $
- $ n ( \text{T}) = 123 $
- $ n ( \text{C}) = 132 $
- $ n ( \text{F} \cap \text{T}) = 58 $
- $ n ( \text{T} \cap \text{C}) = 25 $
- $ n ( \text{F} \cap \text{C}) = 63 $
We know that,
$ n (\text{A} \cup \text{B} \cup \text{C}) = n(\text{A}) + n(\text{B}) + n(\text{C}) – n(\text{A} \cap \text{B}) – n(\text{B} \cap \text{C}) – n(\text{A} \cap \text{C}) + n (\text{A} \cap \text{B} \cap \text{C}) $
Now,
$ n (\text{F} \cup \text{T} \cup \text{C}) = n(\text{F}) + n(\text{T}) + n(\text{C}) – n(\text{F} \cap \text{T}) – n(\text{T} \cap \text{C}) – n(\text{C} \cap \text{F}) + n (\text{F} \cap \text{T} \cap \text{C}) $
$ \Rightarrow 256 = 144 + 123 + 132 – 58 – 25 – 63 + n (\text{F} \cap \text{T} \cap \text{C}) $
$ \Rightarrow n (\text{F} \cap \text{T} \cap \text{C}) = 256 – 253 $
$ \Rightarrow n (\text{F} \cap \text{T} \cap \text{C}) = 3 $
Now, the number of members who can play only tennis $ = n(\text{T}) – n ( \text{F} \cap \text{T}) – n ( \text{T} \cap \text{C}) – n (\text{F} \cap \text{T} \cap \text{C})$
$\qquad = 123 – 58 – 25 + 3 = 43.$
Correct Answer $: \text{D} $