Question

A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 44 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.)

Answer 1

The probability of the presidential candidate selecting three specific capitals out of 44 states is 1 divided by the number of combinations for choosing 3 out of 44, which simplifies to 1/12376.

Step-by-step explanation:

The student is asking about the probability of a presidential candidate selecting a specific route consisting of three capitals out of 44 states. Since the question involves calculating a specific occurrence within a group, it's a combinatorial probability problem. The formula to solve this would be 1 divided by the total number of ways to choose 3 capitals out of 44 without regard to order. The number of ways can be calculated using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of elements to choose from (44 states), and k is the number of elements to pick (3 capitals).

Therefore, the probability P(she selects the route of three specific capitals) is calculated as:

1 / C(44, 3)

1 / (44! / (3! * (44-3)!))

1 / (44! / (3! * 41!))

1 / ((44 * 43 * 42) / (3 * 2 * 1))

1 / (44 * 43 * 42 / 6)

1 / 12376

The probability is thus a simple fraction, 1/12376.