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?

Solution:

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by ⁿC_r and it is given by,

ⁿC_r = n!/ r! (n - r)! where 0 ≤ r ≤ n.

Substituting the values in the formula

⁵C₃ = 5!/ 3! (5 - 3)!

By further calculation

⁵C₃ = (5 × 4 × 3 × 2 × 1)/ (3 × 2 × 2)

⁵C₃ = 10

Therefore, 10 different groups of 3 employees can be chosen.

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?

Summary:

From 5 employees at a company, a group of 3 employees will be chosen to work on a project. 10 different groups of 3 employees can be chosen.