Question

a presidential candidate plans to begin her campaign by visiting the capitals in 3 of 45 states. what is the probability that she selects the route of three specific capitals?
p(she selects the route of three specific capitals) =
(type an integer or a simplified fraction )

Explanation:

Step1: Calculate number of permutations

The number of ways to select and order 3 capitals out of 45 is given by the permutation formula $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 45$ and $r=3$. So $P(45,3)=\frac{45!}{(45 - 3)!}=\frac{45!}{42!}=45\times44\times43=85140$.

Step2: Determine favorable outcomes

There is only 1 favorable outcome (the specific route of three capitals).

Step3: Calculate probability

The probability $P$ is the ratio of the number of favorable outcomes to the total number of outcomes. So $P=\frac{1}{85140}$.

Answer:

$\frac{1}{85140}$