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 ways to choose 3 states out of 45

The number of combinations of choosing $r = 3$ states out of $n=45$ is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$. Here, $C(45,3)=\frac{45!}{3!(45 - 3)!}=\frac{45!}{3!×42!}=\frac{45\times44\times43}{3\times2\times1}=14190$.

Step2: Determine probability

The probability of selecting a specific route (which is 1 particular combination) out of all possible combinations is the ratio of 1 to the total number of combinations. So the probability $P=\frac{1}{14190}$.

Answer:

$\frac{1}{14190}$