NIMCET 2009 Question Paper with solutions

Question : 46 of 120

Marks: +1, -0

"Twelve villages in a district are divided into 3 zones with 4 villages per each zone. The telephone department of the district intends to cornect the villages with telephone lines such 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?

Validate

Solution:

Number of direct lines

=({ }^{4} C_{2} × 3) × 3+{ }^{3} C_{2} ×{ }^{4} C_{1} ×{ }^{4} C_{1} × 2

=6 × 3 × 3+3 × 4 × 4 × 2

=54+96=150

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