A king has unflinching loyalty from eight of his ministers $\text{M1}$ to $\text{M8},$ but he has to select only four to make a cabinet committee. He decides to choose these four such that each selected person shares a liking with at least one of the other three selected. The selected persons must also hate one of the likings of any of the other three persons selected.
- $\text{M1}$ likes fishing and smoking, but hates gambling.
- $\text{M2}$ likes smoking and drinking, but hates fishing.
- $\text{M3}$ likes gambling, but hates smoking.
- $\text{M4}$ likes mountaineering, but hates drinking.
- $\text{M5}$ likes drinking, but hates smoking and mountaineering.
- $\text{M6}$ likes fishing, but hates smoking and mountaineering.
- $\text{M7}$ likes gambling and mountaineering, but hates fishing.
- $\text{M8}$ likes smoking and gambling, but hates mountaineering.
Who are the four people selected by the king?
- $\text{M1, M2, M5, M6}$
- $\text{M3, M4, M5, M6}$
- $\text{M4, M5, M6, M8}$
- $\text{M1, M2, M4, M7}$