To find out how many different groups of 3 employees can be formed from a total of 5 employees, we can use the concept of combinations. Combinations are used when the order of selection does not matter, which is the case here since we are simply selecting a group.
The formula for combinations is given by:
C(n, r) = n! / (r! * (n – r)!)
Where:
- C(n, r) is the number of combinations of n items taken r at a time.
- n is the total number of items (employees, in this case).
- r is the number of items to choose.
- ! denotes factorial, meaning the product of all positive integers up to that number.
In our example, we have:
- n = 5 (the number of employees)
- r = 3 (the number of employees we want to choose)
Plugging these values into the formula gives us:
C(5, 3) = 5! / (3! * (5 – 3)!)
Calculating the factorials:
- 5! = 5 × 4 × 3 × 2 × 1 = 120
- 3! = 3 × 2 × 1 = 6
- (5 – 3)! = 2! = 2 × 1 = 2
Now substituting these values back into the formula:
C(5, 3) = 120 / (6 * 2) = 120 / 12 = 10
Therefore, the number of different groups of 3 employees that can be chosen from a total of 5 employees is 10.