Question

4.18 - a manager wants to evaluate 4 trainees as outstanding, excellent, average, below average and poor. In how many ways can the manager evaluate the four trainees using the five categories?

Answer 1

Solution:

The 4 trainees can be evaluated using the five categories: outstanding, excellent, average, below average and poor

Now, if we view this problem from the perspective of the real world, then every trainee can attain only one category of evaluation according to his/her performance in the training period, i.e. trainee 1 could be either outstanding or excellent or below average or poor or average, he/she cannot be excellent and poor at the same time and similar for others as well

So, in the real world, the result of the evaluation would be 1 way. Although, this 1 way can be any combination of 5 categories (as we do not have actual weights or values in the question to evaluate their actual performance).

The combination could be the following:

Trainee 1 Trainee 2 Trainee 3 Trainee 4

outstanding outstanding outstanding outstanding

excellent

average (5 ways)

below average (5 ways)

poor (5 ways)

( 5 ways) x (5 ways) x (5 ways) x (5 ways) = 625 ways