A small company has 15 employees. Five of these employees will be selected randomly to be interviewed as part of an employee satisfaction program. How many different groups of five can be selected?
3003
To determine the number of different groups of five that can be selected from a pool of 15 employees, we can use the concept of combinations.
The number of combinations of n objects taken r at a time can be calculated using the formula:
C(n, r) = n! / (r!(n - r)!)
Where n represents the total number of objects (employees in this case) and r represents the number of objects to be chosen (number of employees to be selected).
In this case, we need to calculate C(15, 5) because we want to select 5 employees from a pool of 15.
Using the formula, we can calculate it step by step:
C(15, 5) = 15! / (5!(15 - 5)!)
= 15! / (5! * 10!)
To calculate this, we need to know the factorial value of 15 (15!). The factorial of a number is the product of all positive integers less than or equal to that number.
15! = 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
Calculating this value is tedious, so we can use a calculator or a spreadsheet software to get the factorial value.
After calculating 15!, 5!, and 10!, we can substitute these values back into the formula:
C(15, 5) = 15! / (5! * 10!)
Note: The exclamation mark (!) represents factorial.
Simplifying C(15, 5) using the calculated factorial values will give us the final answer, which represents the number of different groups of five that can be selected from a pool of 15 employees.