Twelve villages in a district are divided into 3 zones with 4 villages per zone. The telephone department intends to connect villages so that every two villages in the same zone are connected with three direct lines and every two villages belonging to different zones are connected with two direct lines. How many direct lines are required?
🎥 Video solution / Text Solution of this question is given below:
Within each zone:
Number of pairs among 4 villages = 6 pairs
Each pair has 3 lines → 6 × 3 = 18 lines per zone
3 zones → 18 × 3 = 54 lines
Between zones:
Each zone has 4 villages, so between any two zones: 4×4 = 16 pairs
Each pair has 2 lines → 16×2 = 32 lines per zone-pair