Question

a presidential candidate plans to begin her campaign by visiting the capitals in 3 of 50 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 ways to select 3 states out of 50

The number of permutations of $n$ objects taken $r$ at a time is given by $P(n,r)=\frac{n!}{(n - r)!}$. Here, $n = 50$ and $r=3$, so $P(50,3)=\frac{50!}{(50 - 3)!}=\frac{50!}{47!}=50\times49\times48 = 117600$.

Step2: Determine favorable outcomes

There is only 1 favorable outcome (selecting the specific 3 - state route).

Step3: Calculate probability

The probability $P$ is the ratio of the number of favorable outcomes to the total number of outcomes. So $P=\frac{1}{117600}$.

Answer:

$\frac{1}{117600}$