Question

a presidential candidate plans to begin her campaign by visiting the capitals in 4 of 43 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 43 is given by the permutation formula $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 43$ and $r=4$. So $P(43,4)=\frac{43!}{(43 - 4)!}=\frac{43!}{39!}=43\times42\times41\times40 = 2961840$.

Step2: Determine probability

There is only 1 specific route of the four - capitals. The probability $P$ of selecting this specific route is the number of favorable outcomes (1) divided by the number of total outcomes. So $P=\frac{1}{43\times42\times41\times40}=\frac{1}{2961840}$.

Answer:

$\frac{1}{2961840}$