Accuplacer Practice Test

From 5 employees at a company, a group of 3 employees will be chosen to work on a project. How many different groups of 3 employees can be chosen?

1. 3

2. 5

3. 6

4. 15

The correct answer is: 15

To determine how many different groups of 3 employees can be formed from a total of 5 employees, you can use the concept of combinations. The formula for combinations is given by: \[ C(n, r) = \frac{n!}{r!(n - r)!} \] where \( n \) is the total number of items to choose from (in this case, employees), \( r \) is the number of items to choose (here, the group size), and \( ! \) denotes factorial, which is the product of all positive integers up to that number. In this scenario, you have 5 employees and you want to choose 3: 1. Identify \( n \) and \( r \): - \( n = 5 \) (the employees) - \( r = 3 \) (the number of employees in each group) 2. Substitute into the formula: \[ C(5, 3) = \frac{5!}{3!(5 - 3)!} = \frac{5!}{3! \times 2!} \] 3. Calculate the factorials: - \( 5! = 5 \times 4