Suppose the 10 cities are divided into 4 distinct groups G1, G2, G3, G4 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following:
1) Both cities are in G1
2) Between A and any city in G2
3) Between B and any city in G3
4) Between C and any city in G4
Then the minimum number of direct flights that satisfies the underlying principle of the airline is:___

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Solution

Number of direct flights within the group G1 $=^{3} C_{2} \times 4 = 12$

Number of direct flights between A and any city in G2 $=^{3} C_{1} \times 4 = 12$

Number of direct flights between B and any city in G3 $=^{2} C_{1} \times 4 = 8$

Number of direct flights between C and any city in G4 $=^{2} C_{1} \times 4 = 8$

Hence, Minimum number of direct flights to be scheduled = 12 + 12 + 8 + 8 = 40

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Similar questions

Suppose the 10 cities are divided into 4 distinct groups G1, G2, G3, G4 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following:
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