A country has 10 smart cities. The government | vedclass

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(A) To connect every city to every other city,we need to choose $2$ cities out of $10$ to form a road connection.This is a combination problem where w

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(A) To connect every city to every other city,we need to choose $2$ cities out of $10$ to form a road connection.This is a combination problem where we need to find the number of ways to select $2$ cities from $10$,denoted as $^{10}C_2$.The formula for combinations is $^{n}C_r = \frac{n!}{r!(n-r)!}$.Substituting $n = 10$ and $r = 2$:$^{10}C_2 = \frac{10 	imes 9}{2 	imes 1} = 45$.Therefore,the government needs to construct $45$ roads.

$A$ country has $10$ smart cities. The government decides to connect all these cities by road. How many roads does the government need to construct so that every city is connected to every other city?

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