Question

In a country there are $25$ states Every state has $15$ towns Clearly there will be two kinds of pair of towns one is intra-state and other is inter-state For every intra-state pair there is a network of $2$-highways between that pair of town For inter-state there is network of $3$-highways between that pair of town Calculate the total number of highways in country

• A. $197550$
• B. $207750$
• C. $217550$
• D. $227550$

Answer 1

The correct option is B $207750$

To choose Intra - state pair we have to chose state out of 25 then one town out of 15 then another town out of 15

So

${}^{25}{\text{C}}_2{\times }^{15}{\text{C}}_1{\times }^{15}{\text{C}}_1=67500$

To choose Inter-state pair we have to chose state out of 25 and two town out of 15 so

${}^{25}{\text{C}}_1{\times }^{15}{\text{C}}_2\times =2625$

The total number of highways $=207750$