I would like help with math please

Question

Three baseball cards are selected at random from a group of seven cards. Two cards are rookie cards. What is the probability that exactly one of the three selected cars is a rookie card

Answer 1

First of all we have 3 ways the rookie card could be chosen. (Either first, second or third)

So we have 3 * Probability of choosing one rookie card. In other words we can look at getting the rookie card first and multiply by three because the other ways will be the same probabilities.

So, probability of choosing the rookie card (2/7), times the probability of choosing a non rookie card (5/6), times the probability of choosing another non rookie card (4/5). Notice that these are probabilities without replacement.

3 * 2/7 * 5/6 * 4/5 = 4/7

Alternatively, if you understand the combination function well you can do this:

Total outcome ₇C₃ - That's the number of ways you can choose 3 from 7

Desired outcome ₂C₁ * ₅C₃ - That's number of ways to choose one rookie from 2, and 3 non-rookie from 5

P = ₂C₁ * ₅C₃ / ₇C₃ = 4/7