Question

**Please answer all questions and show all work and calculations. I also have the correct answers and have put them at the end of the question.**

1. The Boston Celtics currently have 20 players on their roster of which nine are guards. Suppose that five players are randomly selected from the Celtics' roster. What is the probability that exactly two of the selected players are guards? Ans: Hypergeometric, 0.383

2. The Boston Celtics currently have 20 players on their roster of which nine are guards. Five of the players will start the game. If the team wants to start 2 guards and 3 other players, how many possible groups of players could be chosen to start the game? Ans: 5,940.

3. How many different FOUR DIGIT numbers can be made by arranging the digits 5 4 3 4 5?

Answer 1

1:

Let X is a random variable shows the number of selected guards. Here X has hypergeometric distribution with parameters as follows:

Population size: N = 20

Number of guards in populations : K = 9

Sample size: n = 5

The required probability is

2:

Number of guards is 9 and number of other players is 20 -9 = 11.

The number of possible groups of players could be chosen to start the game is