Question

a presidential candidate plans to begin her campaign by visiting the capitals in 4 of 41 states. what is the probability that she selects the route of four specific capitals?
p(she selects the route of four specific capitals)=
(type an integer or a simplified fraction.)

Explanation:

Step1: Calculate number of permutations

The number of ways to select and order 4 capitals out of 41 is given by the permutation formula $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 41$ and $r=4$. So $P(41,4)=\frac{41!}{(41 - 4)!}=\frac{41!}{37!}=41\times40\times39\times38$.

Step2: Determine favorable outcomes

There is only 1 favorable outcome (the specific route of 4 capitals).

Step3: Calculate probability

The probability $P$ is the ratio of the number of favorable outcomes to the total number of outcomes. So $P=\frac{1}{41\times40\times39\times38}=\frac{1}{2430360}$.

Answer:

$\frac{1}{2430360}$